Homological mirror symmetry for the quartic surface

By P. Seidel. 2003

216 citations recorded by the source corpus.

This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/27107269c2a02b4c25ee9af765357dcaac71d91b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. D. Auroux
2. L. Katzarkov
3. Nick Sheridan
4. M. Abouzaid
5. P. Seidel
6. T. Bridgeland
7. I. Smith
8. Dmitri Orlov

In Mathematical Physics

1. D. Auroux
2. Nick Sheridan
3. L. Katzarkov
4. M. Abouzaid
5. P. Seidel
6. T. Bridgeland
7. I. Smith
8. Yukinobu Toda

Citations in the corpus

• Generating the Fukaya categories of Hamiltonian 𝐺-manifolds (2015, background): “Finding a split-generator is also the first step in many modern proofs of homological mirror symmetry (for example [7, 57, 59]).”
• Homological mirror symmetry for the genus two curve (2008, background): “There, we now have complete proofs of some cases [44, 49] and partial results for many more [32, 24].”
• Legendrian fronts for affine varieties (2016, methodology): “The general technique of working with Lefschetz bifibrations has been used in the literature for a number of years, see [5, 9, 51, 52, 63, 64, 65].”
• Dirichlet Branes and Mirror Symmetry (2009, methodology): “(Legal disclaimer: There are some technical differences between the definitions given in this text and the definitions needed in Seidel’s paper [420].”
• On the homological mirror symmetry conjecture for pairs of pants (2010, methodology): “One aim of this work is to generalize the arguments of [46] to the Fermat hypersurface in a projective space of arbitrary dimension – we obtain a partial result in Theorem 1.”
• Brane tilings and their applications (2008, background): “1) is demonstrated for two-tori in [219] and quartic K3 surface in [220].”
• Homological mirror symmetry for punctured spheres (2011, background): “ied extensively, and while evidence has been gathered in a number of examples including abelian varieties [16, 28, 23], it has so far only been proved for elliptic curves [34], the quartic K3 surface [37], and their products [7]. Kontsevich was also the first to suggest that homological mirror symmet”
• D-Branes on Calabi-Yau Manifolds (2004, background): “i–Yau threefolds with zero b 1 because of the appearance of extra coisotropic A-branes [46]. This “homological mirror symmetry” statement has been demonstrated for 2-tori [69] and quartic K3 surfaces [71]. 31I thank R. Thomas for discussions on this point. 32This is often called the “derived Fukaya ”
• Handbook of Tilting Theory: Fourier-Mukai transforms (2004, methodology): “related to the symplectic geometryof Y. The homologicalmirrorsymmetry conjecture was recently proved by Seidel for quartic surfaces (which are the simplest Calabi-Yau manifolds after elliptic curves) [71]. Finally this introduction would be incomplete without at least mentioning the celebratedRieman”
• Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, background): “Seidel [63] proved it forM a quartic surface in CP(3) (a Calabi–Yau 2-fold), and Sheridan [65] proved it for M a smooth Calabi–Yau m-fold hypersurface in CP for m > 3.”