73 citations · 265 across the 17 of their papers we have counts for
5 papers · 2 filters
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…