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Homological mirror symmetry for the quartic surface

About this Title

Paul Seidel, Department of Mathematics, MIT, 77 Massachussetts Avenue, Cambridge, Massachusetts 02139

Publication: Memoirs of the American Mathematical Society
Publication Year: 2015; Volume 236, Number 1116
ISBNs: 978-1-4704-1097-1 (print); 978-1-4704-2282-0 (online)
DOI: https://doi.org/10.1090/memo/1116
Published electronically: December 29, 2014
Keywords: Homological mirror symmetry, Floer cohomology, derived category, Lefschetz fibration
MSC: Primary 53D37; Secondary 14D05, 18E30

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Table of Contents

Chapters

  • 1. Introduction
  • 2. $A_{\infty }$-categories
  • 3. Deformation theory
  • 4. Group actions
  • 5. Coherent sheaves
  • 6. Symplectic terminology
  • 7. Monodromy and negativity
  • 8. Fukaya categories
  • 9. Computations in Fukaya categories
  • 10. The algebras $Q_4$ and $Q_{64}$
  • 11. Counting polygons

Abstract

We prove Kontsevich’s form of the mirror symmetry conjecture for (on the symplectic geometry side) a quartic surface in $\mathbb {C} P^3$.

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