The Weil Petersson Geometry Of The Moduli Space Of Sungeqq 3 Calabi Yau Manifolds

Author : Changyong Yin
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (17 download)

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Download or read book Geometry of Calabi-Yau Moduli written by Changyong Yin and published by . This book was released on 2015 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the geometry of the moduli space and the Teichmuller space of Calabi-Yau manifolds, which mainly involves the following two aspects: the (locally, globally) Hermitian symmetric property of the Teichmuller space and the first Chern form of the moduli space with the Weil-Petersson and Hodge metrics. In the first part, we define the notation of quantum correction for the Teichmuller space T of Calabi-Yau manifolds. Under the assumption of vanishing of weak quantum correction, we prove that the Teichmuller space, with the Weil-Petersson metric, is a locally symmetric space. For Calabi-Yau threefolds, we show that the vanishing of strong quantum correction is equivalent to that the image of the Teichmuller space under the period map is an open submanifold of a globally Hermitian symmetric space W of the same dimension as T . Finally, for Hyperka hler manifolds of dimension 2n 4, we find globally defined families of (2, 0) and (2n, 0)-classes over the Teichmu ller space of polarized Hyperkahler manifolds. In the second part, we prove that the first Chern form of the moduli space of polarized Calabi-Yau manifolds, with the Hodge metric or the Weil-Petersson metric, represents the first Chern class of the canonical extensions of the tangent bundle to the compactification of the moduli space with normal crossing divisors.