Hodge Theory of Hypersurfaces in Toric Varieties and Recent Developments in Quantum Physics
Algebraic Geometry
2023-08-30 v1 High Energy Physics - Theory
Commutative Algebra
Combinatorics
Quantum Physics
Abstract
This is the author's Habilitation which took place at University of Essen on July 11, 1993. The manuscript contains two parts. The first one is devoted to the author's combinatorial construction of mirrors of Calabi-Yau hypersurfaces in Gorenstein toric Fano varieties. The second one contains author's results on the variation of mixed Hodge structures of affine hypersurfaces in algebraic tori and their connection to Gelfand-Kapranov-Zelevinsky theory of generalized hypergeometric functions and their applications to the mirror symmetry for Calabi-Yau hypersurfaces in toric varieties.
Keywords
Cite
@article{arxiv.2308.15187,
title = {Hodge Theory of Hypersurfaces in Toric Varieties and Recent Developments in Quantum Physics},
author = {Victor V. Batyrev},
journal= {arXiv preprint arXiv:2308.15187},
year = {2023}
}
Comments
125pages. arXiv admin note: substantial text overlap with arXiv:alg-geom/9310003