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Surfaces With K2 7 And P G 4
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Book Synopsis Surfaces with $K^2 = 7$ and $p_g = 4$ by : Ingrid C. Bauer
Download or read book Surfaces with $K^2 = 7$ and $p_g = 4$ written by Ingrid C. Bauer and published by American Mathematical Soc.. This book was released on 2001 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is the exact description of minimal smooth algebraic surfaces over the complex numbers with the invariants $K DEGREES2 = 7$ und $p_g = 4$. The interest in this fine classification of algebraic surfaces of general type goes back to F. Enriques, who dedicates a large part of his celebrated book Superficie Algebriche to this problem. The cases $p_g = 4$, $K DEGREES2 \leq 6$ were treated in the past by several authors (among others M. Noether, F. Enriques, E. Horikawa) and it is worthwhile to remark that already the case $K DEGREES2 = 6$ is rather complicated and it is up to now not possible to decide whether the moduli space of these surfaces
Book Synopsis Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces by : Linus Kramer
Download or read book Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces written by Linus Kramer and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title classifys 1-connected compact homogeneous spaces which have the same rational cohomology as a product of spheres $\mahtbb{S} DEGREES{n_1}\times\mathbb{S} DEGREES{n_2}$, with $3\leq n_1\leq n_2$ and $n_2$ odd. As an application, it classifys compact generalized quadrangles (buildings of type $C_2)$ which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one f
Book Synopsis Recent Advances in Hodge Theory by : Matt Kerr
Download or read book Recent Advances in Hodge Theory written by Matt Kerr and published by Cambridge University Press. This book was released on 2016-02-04 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.
Book Synopsis Compact Complex Surfaces by : W. Barth
Download or read book Compact Complex Surfaces written by W. Barth and published by Springer. This book was released on 2015-05-22 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
Download or read book Complex Geometry written by Ingrid Bauer and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves.
Book Synopsis Global Aspects of Complex Geometry by : Fabrizio Catanese
Download or read book Global Aspects of Complex Geometry written by Fabrizio Catanese and published by Springer Science & Business Media. This book was released on 2006-09-29 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry
Book Synopsis Geometry and Complex Variables by : S. Coen
Download or read book Geometry and Complex Variables written by S. Coen and published by Routledge. This book was released on 2017-11-22 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.
Book Synopsis Basic Global Relative Invariants for Homogeneous Linear Differential Equations by : Roger Chalkley
Download or read book Basic Global Relative Invariants for Homogeneous Linear Differential Equations written by Roger Chalkley and published by American Mathematical Soc.. This book was released on 2002 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Book Synopsis Derived $\ell $-Adic Categories for Algebraic Stacks by : Kai Behrend
Download or read book Derived $\ell $-Adic Categories for Algebraic Stacks written by Kai Behrend and published by American Mathematical Soc.. This book was released on 2003 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Book Synopsis Noether-Lefschetz Problems for Degeneracy Loci by : Jeroen Spandaw
Download or read book Noether-Lefschetz Problems for Degeneracy Loci written by Jeroen Spandaw and published by American Mathematical Soc.. This book was released on 2003 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the cohomology of degeneracy loci. This title assumes that $E\otimes F DEGREES\vee$ is ample and globally generated, and that $\psi$ is a general homomorphism. In order to study the cohomology of $Z$, it considers the Grassmannian bundle $\pi\colon Y: =\mathbb{G}(f-r, F)\to X$ of $(f-r)$-dimensional linear subspaces of the fibre
Book Synopsis Limit Theorems for Null Recurrent Markov Processes by : Reinhard Höpfner
Download or read book Limit Theorems for Null Recurrent Markov Processes written by Reinhard Höpfner and published by American Mathematical Soc.. This book was released on 2003 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Geometry: Hirzebruch 70 by : Friedrich Hirzebruch
Download or read book Algebraic Geometry: Hirzebruch 70 written by Friedrich Hirzebruch and published by American Mathematical Soc.. This book was released on 1999 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference on algebraic geometry in honor of Professor Friedrich Hirzebruch's 70th Birthday. The event was held at the Stefan Banach International Mathematical Center in Warsaw (Poland). Topics covered in the book include intersection theory, singularities, low-dimensional manifolds, moduli spaces, number theory, and interactions between mathematical physics and geometry. Also included are articles from notes of two special lectures. The first, by Professor M. Atiyah, describes the important contributions to the field of geometry by Professor Hirzebruch. The second article contains notes from the talk delivered at the conference by Professor Hirzebruch. Contributors to the volume are leading researchers in the field.
Book Synopsis Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion by : Mikhail Anatolʹevich Lifshit︠s︡
Download or read book Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion written by Mikhail Anatolʹevich Lifshit︠s︡ and published by American Mathematical Soc.. This book was released on 2002 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.
Book Synopsis Almost Commuting Elements in Compact Lie Groups by : Armand Borel
Download or read book Almost Commuting Elements in Compact Lie Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2002 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Book Synopsis Some Generalized Kac-Moody Algebras with Known Root Multiplicities by : Peter Niemann
Download or read book Some Generalized Kac-Moody Algebras with Known Root Multiplicities written by Peter Niemann and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Book Synopsis Mutual Invadability Implies Coexistence in Spatial Models by : Richard Durrett
Download or read book Mutual Invadability Implies Coexistence in Spatial Models written by Richard Durrett and published by American Mathematical Soc.. This book was released on 2002 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.
Book Synopsis Triangulations of Oriented Matroids by : Francisco Santos
Download or read book Triangulations of Oriented Matroids written by Francisco Santos and published by American Mathematical Soc.. This book was released on 2002 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
