2 citations · 2 across the 1 of their papers we have counts for
7 papers
Quotient singularities, integer ratios of factorials and the Riemann Hypothesis
Alexander Borisov
The goal of this paper is to reveal a close connection between the following three subjects that have not been studied together in the past: terminal and canonical cyclic quotient…
On a Question of Craven and a Theorem of Belyi
Alexandr Borisov
In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\Q$ if and only if all of its irrational ro…
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…
Positive positive-definite functions and measures on locally compact abelian groups
Alexandr Borisov
The author was recently able to provide a cohomological interpretation of Tate's Riemann-Roch formula for number fields using some new harmonic analysis objects, ghost-spaces. When…
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…