73 citations · 265 across the 17 of their papers we have counts for
17 papers
A family of K3 surfaces and towers of algebraic curves over finite fields
Sergey Galkin, Sergey Rybakov
For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good…
On pairs, triples and quadruples of points on a cubic surface
Sergey Galkin, Pavel Popov
Let denote -th symmetric power of a cubic surface . We show that is stably birational to , despite examples when is not…
Degenerations, transitions and quantum cohomology
Sergey Galkin
Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing G…
Fano-Mathieu correspondence
Sergey Galkin
We show that -Fano threefolds are mirror-modular. 1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of . 2. Quantum periods, shifted by…
Small toric degenerations of Fano threefolds
Sergey Galkin
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.
Examples violating Golyshev's canonical strip hypotheses
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomial…
On automorphic forms of small weight for fake projective planes
Sergey Galkin, Ilya Karzhemanov, Evgeny Shinder
On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-to…
Gamma conjecture via mirror symmetry
Sergey Galkin, Hiroshi Iritani
The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamm…
On a zeta-function of a dg-category
Sergey Galkin, Evgeny Shinder
We define a zeta-function of a pre-triangulated dg-category and investigate its relationship with the motivic zeta-function in the geometric case.
The Fano variety of lines and rationality problem for a cubic hypersurface
Sergey Galkin, Evgeny Shinder
We find a relation between a cubic hypersurface and its Fano variety of lines in the Grothendieck ring of varieties. We prove that if the class of an affine line is not…
Quantum Periods For Certain Four-Dimensional Fano Manifolds
Tom Coates, Sergey Galkin, Alexander Kasprzyk +1
We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all…
Dubrovin's conjecture for
Sergey Galkin, Anton Mellit, Maxim Smirnov
We show that the big quantum cohomology of the symplectic isotropic Grassmanian is generically semisimple, whereas its small quantum cohomology is known to be non-semisim…
The conifold point
Sergey Galkin
Consider a Laurent polynomial with real positive coefficients such that the origin is strictly inside its Newton polytope. Then it is strongly convex as a function of real positive…
Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures
Sergey Galkin, Vasily Golyshev, Hiroshi Iritani
We propose Gamma Conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum diff…
Minifolds and Phantoms
Sergey Galkin, Ludmil Katzarkov, Anton Mellit +1
A minifold is a smooth projective -dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an except…
Quantum Periods for 3-Dimensional Fano Manifolds
Tom Coates, Alessio Corti, Sergey Galkin +1
The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the…
Exceptional collections of line bundles on the Beauville surface
Sergey Galkin, Evgeny Shinder
We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface . These quasi-phantoms subcategories appear as right ort…