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Homological Mirror Symmetry for the Genus 2 Curve in an Abelian Variety and Its Generalized Strominger-Yau-Zaslow Mirror

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서명/저자사항Homological Mirror Symmetry for the Genus 2 Curve in an Abelian Variety and Its Generalized Strominger-Yau-Zaslow Mirror.
개인저자Cannizzo, Catherine Kendall Asaro.
단체저자명University of California, Berkeley. Mathematics.
발행사항[S.l.]: University of California, Berkeley., 2019.
발행사항Ann Arbor: ProQuest Dissertations & Theses, 2019.
형태사항145 p.
기본자료 저록Dissertations Abstracts International 81-03B.
Dissertation Abstract International
ISBN9781085784672
학위논문주기Thesis (Ph.D.)--University of California, Berkeley, 2019.
일반주기 Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Advisor: Auroux, Denis.
이용제한사항This item must not be sold to any third party vendors.This item must not be added to any third party search indexes.
요약Motivated 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.
일반주제명Mathematics.
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