Mirror stability conditions and SYZ conjecture for Fermat polynomials
So Okada
TL;DR
This paper explores the mirror symmetry of Fermat Calabi-Yau varieties through stability conditions and Lagrangian vanishing cycles, linking geometric and categorical perspectives in mirror symmetry.
Contribution
It introduces a novel framework connecting mirror stability conditions with Lagrangian connect sums and quiver representations in the context of Fermat Calabi-Yau varieties.
Findings
Calabi-Yau Fermat varieties derived from Lagrangian connect sums
Stability conditions correspond to graded Lagrangian vanishing cycles
Mirror symmetry relates these cycles to quiver representations
Abstract
Calabi-Yau Fermat varieties are obtained from moduli spaces of Lagrangian connect sums of graded Lagrangian vanishing cycles on stability conditions on Fukaya-Seidel categories. These graded Lagrangian vanishing cycles are stable representations of quivers on their mirror stability conditions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry