자료유형 | 학위논문 |
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서명/저자사항 | Homological Mirror Symmetry for the Genus 2 Curve in an Abelian Variety and Its Generalized Strominger-Yau-Zaslow Mirror. |
개인저자 | Cannizzo, Catherine Kendall Asaro. |
단체저자명 | University of California, Berkeley. Mathematics. |
발행사항 | [S.l.]: University of California, Berkeley., 2019. |
발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
형태사항 | 145 p. |
기본자료 저록 | Dissertations Abstracts International 81-03B. Dissertation Abstract International |
ISBN | 9781085784672 |
학위논문주기 | Thesis (Ph.D.)--University of California, Berkeley, 2019. |
일반주기 |
Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Advisor: Auroux, Denis. |
이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
요약 | Motivated by observations in physics, mirror symmetry is the concept that certain manifolds come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry on Y. It allows one to deduce information about Y from known properties of X. Strominger-Yau-Zaslow (1996) described how such pairs arise geometrically as torus fibrations with the same base and related fibers, known as SYZ mirror symmetry. Kontsevich (1994) conjectured that a complex invariant on X (the bounded derived category of coherent sheaves) should be equivalent to a symplectic invariant of Y (the Fukaya category). This is known as homological mirror symmetry. In this project, we first use the construction of SYZ mirrors for hypersurfaces in abelian varieties following Abouzaid-Auroux-Katzarkov, in order to obtain X and Y as manifolds. The complex manifold comes from the genus 2 curve as a hypersurface in its Jacobian torus, and we equip the SYZ mirror manifold with a symplectic form. We then describe an embedding of the category on the complex side into a cohomological Fukaya-Seidel category of Y as a symplectic fibration. While our fibration is one of the first nonexact, non-Lefschetz fibrations to be equipped with a Fukaya category, the main geometric idea in defining it is the same as in Seidel's construction for Fukaya categories of Lefschetz fibrations. |
일반주제명 | Mathematics. |
언어 | 영어 |
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