47 citations · 61 across the 4 of their papers we have counts for
13 papers
Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
Victor Batyrev, Maximilian Kreuzer
In this paper, we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among…
The Cox Ring of a Del Pezzo Surface Has Rational Singularities
Oleg N. Popov
For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, cal…
The Cox ring of a Del Pezzo surface
Victor V. Batyrev, Oleg N. Popov
Let be a smooth Del Pezzo surface obtained from by blowing up points in general position. It is well known that for the Picard group…
Mixed toric residues and Calabi-Yau complete intersections
Victor V. Batyrev, Evgeny N. Materov
Using Cayley trick, we define the notions of mixed toric residues and mixed Hessians associated with Laurent polynomials .We conjecture that the values of mixed to…
Toric Residues and Mirror Symmetry
Victor V. Batyrev, Evgeny N. Materov
We develop some ideas of Morrison and Plesser and formulate a precise mathematical conjecture which has close relations to toric mirror symmetry. Our conjecture, we call it Toric R…
Canonical abelianization of finite group actions
Victor V. Batyrev
In these notes we present a corrected version of the algorithm for abelianization of stabilizers of finite group actions on smooth manifolds using equivariant blow ups.