On-line mathematical papers of Askold Khovanskii

On analogues of Alexandrov-Fenchel inequalities for hyperbolic forms, "Doclady AN SSSR", V. 276, N 6, 1332-1334, 1984; translation in Soviet Math. Dokl. V. 29(1984), no. 3. PDF (English).

Newton Polyhedra (algebra and geometry), Proceedings of XIII All-Union School on the Operator Theory in Functional Spaces, Kujbishev, 202-221, 1989; translation in Amer. Math. Soc. Transl. (2) V. 153, 1992, 183--199. PDF (English).

Sums of finite sets, orbits of commutative semigroups and Hilbert function, "Funkts. analiz", V. 29, N. 2, 36-50, 1995; translation in Funct. Anal. Appl. 29 (1995), no. 2, 102-112. PDF (Russian)

(with O. Gelfond) Newton polyhedra and Grothendieck residues "Doklady RAN'', V. 3, N. 350, 298-300, 1996; translation in Doklady Mathematics v 54, no. 2, 1996, 700-702. PDF (Russian). PDF (English).

(with S. Zdravkovska) Branched covers of $S^2$ and braid groups, "Journal of Knot Theory and its Ramifications", V. 5, N. 1, 55-75, 1996. PDF (English).

Prilozhenie 3: Razdelyayushchie resheniya i otnoshenie poryadka (Appendix 3: Separating solutions and the relation of order). From the Russian text of the book "Fewnomials", "PHASIS Publishing House", Moscow, 1997, 198-207). PDF (Russian).

Consistent partitions of polytopes and polynomial measures, Topics in Singularity Theory: V.I. Arnold's 60th Anniversary Collection, Amer. Math. Soc. Transl., Ser. 2, Vol. 180, Amer. Math. Soc., Providence, RI, 1997, 157-166. PDF (Russian). PDF (English).

Newton polygons, curves on torus surfaces, and the converse Weil theorem, "Uspekhi matematicheskikh nauk'', V. 52, No 6(318), 113-142, 1997; translation in Russian Math. Surveys 52 (1997), no. 6, 1251-1279. PDF (Russian) . PostScript (English).

On a lemma of Kontsevich, "Funkts. analiz", V. 31, N. 4, 89-91, 1997; translation in Funct. Anal. Appl. 31 (1997), no. 4, 296-298 (1998). PDF (Russian). PostScript (English).

Boundary indexes of 1-forms with homogeneous polynomial coefficients, "Algebra and Analysis'', V.10, N.3, 1998, 193-222; translation in St. Petersburg Math. J. 10 (1999), no. 3, 553-575. PDF (Russian).

(with Andrei Gabrielov) Multiplicity of a Noetherian Intersection Geometry of Differential Equations, Amer. Math. Soc. Transl., Ser. 2, Vol. 186, Amer. Math. Soc., Providence, RI, 1998, 119-130. PDF (English).

Newton polyhedrons, a new formula for mixed volume, product of roots of a system of equations, Proceedings of a Conference in Honour of V.I. Arnold for his Sixtieth Birthday, Fields Institute Communicatins, Vol. 24, Amer. Math. Soc., Providence, RI, 1999, 325-364. PDF (English).

Families of sections of quadrics and classical geometries, "Funkts. analiz", V. 34, N.3, 91-95, 2000; translation in Funct. Anal. Appl. 34 (2000), no. 3, 235-238 (2000). PDF (Russian) . PDF (Englich) .

Geometricheskie obobshcheniya zadachi o preobrazovanii nomogramm iz vyrovnennykh tochek v tsirkulp1nye nomogrammy (Geometrical generalizations of a problem about transformation of the nomograms consisting of aligned points into nomograms consisting of equidistant points). Nomography collection, No.17, RAN, Vychisl. Tsentr, 73-88, 2000. PDF (Russian).

On the continuability of multivalued analytic functions to an analytic subset, "Funkts. analiz", V. 35, N.1, 62-73, 2001; translation in Funct. Anal. Appl. 35 (2001), no. 1, 51-59 (2001). PDF (Russian). PDF (English).

(with O.A.Gelfond) Toric geometry and Grothendieck residues, "Moscow Mathematical Jornal", V. 2, No 1, 2002, 99-112. PDF (English).

On the nonrepresentability of functions of several variables by quadratures "Funkts. analiz", Vol. 37, No 4, 2003, 74-85; translation in Funct. Anal. Appl. 37 (2003), no. 4, 302-310 (2003). PDF (Russian). PDF (English).

On solvability and unsolvability of equations in explicit form, "Uspehi Matem. Nauk", Vol. 59, No. 4(358), 2004, 69-146; translation in Russian Math. Surveys 59 No. 4 (2004), 661-736. PostScript (Russian). PDF (English).

Logarithmic Functional and the Weil Reciprocity Law. Proceedings of the Waterloo Workshop on Computer Algebra, 2006, Ed: Kotsireas I, Zima E., World Scientific Press, 85-108, 2007. PDF (English).

Variations on solvability by radicals. Trudy Matematicheskogo instituta im. Steklova, Vol. 259, 86-105 (2007); translation in Proceedings of the Steklov Institute of Mathematics. PDF (Russian). PDF (English).

(with A. Esterov) Elimination theory and Newton polyhedra. Functional Analysis and Other Mathematics, Springer Berlin/Heidelberg, Vol. 2, No 1 December, 2008 45-71. PDF (English).

Logarithmic functional and reciprocity laws. In book: Toric Topology. International Conference May 28-June 3, 2006. Osaka City University. Osaka, Japan. Contemporary Mathematics. Vol. 460, 221-229, Amer. Math. Soc., Providence, RI, 2008. PDF (English).

(with Yu. Burda) Degree of rational mapping, and the theorems of Sturm and Tarski. Journal of Fixed Point Theory and Applications. Vol. 3, No. 1, 2008, 79-93. PDF (English).

Polyhedra and algebra. Trudy Instituta sistemnogo analiza RAN. V. 38, 2008, 23-35. PDF (Russian).

(with K. Kaveh) Convex bodies and algebraic equations on affine varieties. 44 pp. arXiv:0804.4095 (April 2008).

(with K. Kaveh) Algebraic equations and convex bodies. 16 pp. arXiv:0812.4688 (December 2008) "Perspectives in Analysis, Geometry and Topology". Progress in Mathematics series of Birkhauser. (Accepted).

(with K. Kaveh) Mixed volume and an analogue of intersection theory of divisors for non-complete varieties. 34 pp. arXiv:0812.0433 (December 2008). Moscow Mathematical Journal. (Accepted).

(with K. Kaveh) Newton convex bodies, semigroups of integral points, graded algebras and intersection theory. 49 pp. arXiv:0904.3350v1 (April 2009).