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:
Geometrically Nilpotent Subvarieties. Finite Fields Appl. 50 (2018), 366--371.
Iterations of Integer Polynomial Maps Modulo Primes. J. Integer Sequences 16 (2013), no. 8, Article 13.8.3.
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). Proc. Amer. Math. Soc. 142 (2014), no. 11, 3687--3694.
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.
Directional rational approximations with some applications to algebraic geometry (with V.V. Shokurov). [Russian] Tr. Mat. Inst. Steklova 240 (2003), Biratsion. Geom. Linein. Sist. Konechno Porozhdennye Algebry, 73--81; translation in Proc. Steklov Inst. Math. 2003, no. 1 (240), 66--74.
Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint. Preprint (1999).
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.
Singular toric Fano varieties (with Lev Borisov). [Russian] Mat. Sbornik 183 (1992), no. 2, 134--141; translation in Russian Acad. Sci. Sb. Math. 75 (1993), no. 1, 277--283.

Two-dimensional Jacobian Conjecture and Related Topics:
Frameworks for Two-dimensional Keller Maps. Electronic Journal of Combinatorics 27 (3) (2020), 3.54.
On the Stein factorization of resolutions of two-dimensional Keller maps. Beitr. Algebra Geom. 56 (2015), no. 1, 299--312.
On two invariants of divisorial valuations at infinity. J. Algebraic Combinatorics 39 (2014), no. 3, 691--710.
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 (1999).
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:
Corrigendum to "Quantum integers and cyclotomy'' [J. Number Theory 109 (1) (2004) 120–135] [MR2098480]. J. Number Theory 145 (2014), 632--634.
Quantum integers and cyclotomy (with Melvyn Nathanson and Yang Wang). J. Number Theory 109 (2004), no. 1, 120--135.
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 (with M. Filaseta, T.-Y. Lam, and O. Trifonov). Acta Arithmetica 90 (1999), no. 2, 121--153.
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.