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Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint
Alexandr Borisov
It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P in R^k of positive finite volume, such that in…
Boundedness of Fano threefolds with log-terminal singularities of given index
Alexandr Borisov
We prove the boundedness theorem for Fano threefolds with log-terminal singularities of any fixed index. This is an improvement of our earlier result, where we required additionall…
Convolution structures and arithmetic cohomology
Alexandr Borisov
In this paper we construct arithmetic analogs of the Riemann-Roch theorem and Serre's duality for line bundles. This improves on the works of Tate and van der Geer - Schoof. We def…
On classification of toric singularities
Alexander Borisov
In 1988 S. Mori, D. Morrison, and I. Morrison gave a computer-based conjectural classification of four-dimensional cyclic quotient singularities of prime index. It was partially pr…