103 citations · 686 across the 101 of their papers we have counts for
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Noncommutative two-tori with real multiplication as noncommutative projective varieties
Alexander Polishchuk
We define analogues of homogeneous coordinate algebras for noncommutative two-tori with real multiplication. We prove that the categories of standard holomorphic vector bundles on…
Noncommutative Proj and coherent algebras
Alexander Polishchuk
We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the…
Categories of holomorphic vector bundles on noncommutative two-tori
Alexander Polishchuk, Albert Schwarz
In this paper we study the category of standard holomorphic vector bundles on a noncommutative two-torus. We construct a functor from the derived category of such bundles to the de…
Minimal representations: spherical vectors and automorphic functionals
David Kazhdan, Alexander Polishchuk
In the first part of this paper we study minimal representations of simply connected simple split groups of type or over local non-archimedian fields. Our main result i…
Witten's top Chern class on the moduli space of higher spin curves
Alexander Polishchuk
This paper is a sequel to math.AG/0011032. Its goal is to show that Witten's "top Chern class" constructed in loc.cit. satisfies all the axioms of math.AG/9905034.
A_{infinity}-structures, Brill-Noether loci and the Fourier-Mukai transform
Alexander Polishchuk
We use A_{infinity}-formalism to study variation of cohomology spaces under formal deformations of coherent sheaves on projective varieties. As an application we describe formal ne…