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Singular Lefschetz pencils

- D. Auroux, S. Donaldson, L. Katzarkov
- Mathematics
- 14 October 2004

We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4–manifold equipped with a “near-symplectic” structure (ie, a closed 2–form which is symplectic outside a… Expand

Flat surfaces and stability structures

- F. Haiden, L. Katzarkov, M. Kontsevich
- Mathematics
- 30 September 2014

We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is… Expand

Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves

- D. Auroux, L. Katzarkov, D. Orlov
- Mathematics
- 9 June 2005

We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface Xk… Expand

Families of K3 surfaces

- R. Borcherds, L. Katzarkov, T. Pantev, N. Shepherd-barron
- Mathematics
- 26 January 1997

We use automorphic forms to prove that a compact family of Kaehler K3 surfaces with constant Picard number is isotrivial.

Variation of geometric invariant theory quotients and derived categories

- M. Ballard, David Favero, L. Katzarkov
- MathematicsJournal für die reine und angewandte Mathematik…
- 29 March 2012

We study the relationship between derived categories of factorizations on gauged Landau–Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions… Expand

Mirror symmetry for weighted projective planes and their noncommutative deformations

- D. Auroux, L. Katzarkov, D. Orlov
- Mathematics
- 15 April 2004

We study the derived categories of coherent sheaves of weighted projective spaces and their noncommutative deformations, and the derived categories of Lagrangian vanishing cycles of their mirror… Expand

Dynamical systems and categories

- G. Dimitrov, F. Haiden, L. Katzarkov, M. Kontsevich
- Mathematics
- 31 July 2013

We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and… Expand

Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

- L. Katzarkov, M. Kontsevich, T. Pantev
- Mathematics
- 21 September 2014

In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the… Expand

Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves

- D. Auroux, S. Donaldson, L. Katzarkov
- Mathematics
- 2 June 2002

Abstract. We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide a purely… Expand

Hodge theoretic aspects of mirror symmetry

- L. Katzarkov, M. Kontsevich, T. Pantev
- Mathematics
- 31 May 2008

We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of… Expand

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