Holmstrom Mirror symmetry

Many things in folder AG/Mirror symmetry

HMS for toric varieties: Abouzaid

http://mathoverflow.net/questions/40062/roadmap-for-mirror-symmetry

Meet HMS: http://arxiv.org/abs/0801.2014

HMS: See all by Seidel, books and arXiv

Names: Katzarkov, Sheridan, Orlov, Kontsevich. Orlov has a couple of surveys on arxiv.

MR2336692 (2008h:53151) Neeman, Amnon An infinite version of homological mirror symmetry. Real and complex singularities, 290–298, World Sci. Publ., Hackensack, NJ, 2007

Seidel book: Fukaya categories and Picard-Lefschetz theory

http://mathoverflow.net/questions/2905/is-the-fukaya-category-defined

arXiv:0908.1256 String modular motives of mirrors of rigid Calabi-Yau varieties from arXiv Front: math.AG by Savan Kharel, Monika Lynker, Rolf Schimmrigk The modular properties of some higher dimensional varieties of special Fano type are analyzed by computing the L-function of their $\Omega-$motives. It is shown that the emerging modular forms are string theoretic in origin, derived from the characters of the underlying rational conformal field theory. The definition of the class of Fano varieties of special type is motivated by the goal to find candidates for a geometric realization of the mirrors of rigid Calabi-Yau varieties. We consider explicitly the cubic sevenfold and the quartic fivefold, and show that their motivic L-functions agree with the L-functions of their rigid mirror Calabi-Yau varieties. We also show that the cubic fourfold is string theoretic, with a modular form that is determined by that of an exactly solvable K3 surface.

[arXiv:0907.3903] Homological mirror symmetry for curves of higher genus from arXiv Front: math.AG by Alexander I. Efimov Katzarkov has proposed a generalization of Kontsevich’s mirror symmetry conjecture, covering some varieties of general type. Seidel [Se] has proved a version of this conjecture in the simplest case of the genus two curve. Basing on the paper of Seidel, we prove the conjecture (in the same version) for curves of genus $g\geq 3,$ relating the Fukaya category of a genus $g$ curve to the category of Landau-Ginzburg branes on a certain singular surface. We also prove a kind of reconstruction theorem for hypersurface singularities. Namely, formal type of hypersurface singularity (i.e. a formal power series up to a formal change of variables) can be reconstructed, with some technical assumptions, from its D$(\Z/2)$-G category of Landau-Ginzburg branes. The precise statement is Theorem 1.2.

[arXiv:0910.2014] Homological mirror symmetry of Fermat polynomials from arXiv Front: math.AG by So Okada 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.

nLab page on Mirror symmetry?