Alexander Borisov's Publications and Preprints

My publications and selected preprints are listed below, roughly classified by the subject matter. Some texts may differ slightly from the final published versions.

Iterations of Polynomial Maps, with Applications to Group Theory:
Iterarions of Integer Polynomial Maps Modulo Primes. Preprint (2013). J. Integer Sequences, to appear.
Polynomial maps over p-adics and residual properties of mapping tori of group endomorphisms, (with M. Sapir). Int. Math. Res. Not. IMRN (2009) no.16, 3002--3015.
Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms, (with M. Sapir). Inventiones Math., 160 (2005) no.2, 341--356.

Toric Varieties and Lattice Polytopes:
On the log discrepancies in Mori contractions (with Valery Alexeev). Preprint (2012). Proc. Amer. Math. Soc., to appear.
On Empty Lattice Simplices in Dimension 4 (with Margherita Barile, Dominique Bernardi, and Jean-Michel Kantor). Proc. Amer. Math. Soc., 139 (2011), no. 12, 4247--4253.
Quotient singularities, integer ratios of factorials and the Riemann Hypothesis, Int. Math. Res. Not. IMRN 2008 (2005) no.15, Art. ID rnn052 (19 pages).
Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint, preprint.
On classification of toric singularities, Algebraic Geometry. 9. J. Math. Sci. (New York) 94 (1999), no. 1, 1111--1113.
Minimal discrepancies of toric singularities, Manuscripta Math. 92 ( 1997 ), no. 1, 33 -- 45.

Two-dimensional Jacobian Conjecture and Related Topics:
On two invariants of divisorial valuations at infinity. Preprint (2012). J. Algebraic Combinatorics, to appear.
On the Stein factorization of resolutions of Jacobian self-maps of P^2. Preprint (2012). Submitted.
On Resolution of Compactifications of Unramified Planar Self-maps. Preprint (2011-12). Unpolished, will not be submitted.

Applications of Harmonic Analysis to Number Theory:
Positive positive-definite functions and measures on locally compact abelian groups, preprint.
Convolution structures and arithmetic cohomology, Compositio Math., 136 (2003), no. 3, 237--254.

Fano Varieties:
Boundedness of Fano threefolds with log-terminal singularities of given index, J. Math. Sci. Univ. Tokyo, 8 (2001), no. 2, 329--342.
Boundedness theorem for Fano log-threefolds, J. Algebraic Geom. 5 (1996), no. 1, 119--133.

Rational Polynomials:
On a Question of Craven and a Theorem of Belyi, Proc. Amer. Math. Soc. 131 (2003), no. 12, 3677--3679.
Classes of polynomials having only one non-cyclotomic irreducible factor, Acta Arithmetica, 90 (1999), no. 2, 121--153 (with
M. Filaseta, T.-Y. Lam, and O. Trifonov)
On some polynomials allegedly related to the abc conjecture, Acta Arithmetica, 84 (1998), no. 2, 109--128.

A congruence Problem for Polyhedra (with Mark Dickinson and Stuart Hastings)Amer. Math. Monthly 131 (2010) 232--249.