7 papers
On K-Stability of Reductive Varieties
Valery Alexeev, Ludmil Katzarkov
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don…
Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves
D. Auroux, S. K. Donaldson, L. Katzarkov
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…
Fundamental groups of complements of plane curves and symplectic invariants
D. Auroux, S. K. Donaldson, L. Katzarkov +1
Introducing the notion of stabilized fundamental group for the complement of a branch curve in , we define effectively computable invariants of symplectic 4-manifolds that ge…
Deformations of large fundamental groups
B. de Oliveira, L. Katzarkov, M. Ramachandran
A projective variety has a large fundamental group if its universal covering has no compact subvarieties. In this paper we investigate whether the property of a variety having a la…
Hyperelliptic Szpiro inequality
F. Bogomolov, L. Katzarkov, T. Pantev
We generalize the classical Szpiro inequality to the case of a semistable family of hyperelliptic curves. We show that for a semistable symplectic Lefschetz fibration of hyperellip…
Nonabelian mixed Hodge structures
Ludmil Katzarkov, Tony Pantev, Carlos Simpson
We propose a definition of ``nonabelian mixed Hodge structure'' together with a construction associating to a smooth projective variety and to a nonabelian mixed Hodge structur…