Homological mirror symmetry of Fermat polynomials
So Okada
TL;DR
This paper explores the homological mirror symmetry for Fermat polynomials, establishing derived Morita equivalences between algebraic and symplectic categories, and examining related structures like stability conditions and Hochschild homologies.
Contribution
It demonstrates a derived Morita equivalence for Fermat polynomials' categories and investigates associated structures such as stability conditions and modular forms.
Findings
Establishes derived Morita equivalence between categories
Analyzes stability conditions and modular forms related to Fermat polynomials
Connects Hochschild homologies with mirror symmetry
Abstract
We discuss homological mirror symmetry of Fermat polynomials in terms of derived Morita equivalence between derived categories of coherent sheaves and Fukaya-Seidel categories (a.k.a. perfect derived categories of directed Fukaya categories), and some related aspects such as stability conditions, (kinds of) modular forms, and Hochschild homologies.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra