List of Publications: Mikhail Kapranov

  1. The derived category of coherent sheaves on Grassmann varieties, Functional Analysis and Applications 17 (1983), 145--146.
  2. On the derived category of coherent sheaves on Grassmann varieties, Mathematics of USSR - Izvestija, 24 (1985), 183--192.
  3. (with Y. I. Manin) Twistor transform and algebro-geometric constructions of solutions to field theory equations, Russian Mathematical Surveys, 41 no. 5 (1986), 85--107.
  4. The derived category of coherent sheaves on a quadric, Funct. Anal. and Appl. 20 (1986), 141--142.
  5. On cuspidal divisors on modular varieties of elliptic modules, Math. USSR Izv. 30 (1988), 533--547.
  6. On the derived category and K-functor of coherent sheaves on intersections of quadrics, Math. USSR Izv. 32 (1989), 191--204.
  7. On the derived categories of coherent sheaves on some homogeneous spaces, Inventiones Mathematicae 92 (1988), 479--508.
  8. (with I. M. Gelfand, A. V. Zelevinsky) Equations of hypergeometric type and Newton polytopes, Soviet Mathematics -- Doklady, 37 (1988), 678--683].
  9. (with I. M. Gelfand, A. V. Zelevinsky) Hypergeometric functions and toric varieties, Funct. Anal. and Appl. 23 no. 2 (1989), 12--26.
  10. (with I. M. Gelfand, A. V. Zelevinsky) A-discriminants and Cayley-Koszul complexes, Sov. Math. Dokl. 40 (1990), 239--243.
  11. (with A. I. Bondal) Representable functors, Serre functors and mutations, Math. USSR Izvestija, 35 (1990), 519--541.
  12. (with I. M. Gelfand, A. V. Zelevinsky) Projectively dual varieties and hyperdeterminants, Sov. Math. Dokl. 39 no. 2 (1989), 385--389.
  13. (with I. M. Gelfand, A. V. Zelevinsky) Newton polyhedra of principal A-determinants, Soviet Math. Dokl. 40 (1990), 278--281.
  14. On non-holonomic D-modules and non-constructible perverse sheaves, Funct. Anal. and Appl. 23 (1989), 325--326.
  15. (with I. M. Gelfand, A. V. Zelevinsky) On discriminants of polynomials in several variables, Funct. Anal. and Appl. 24 no. 1 (1990), 1--4.
  16. Mutations and Serre functors in constructible sheaves, Funct. Anal. and Appl. 24 (1990), 155--156.
  17. (with I. M. Gelfand, A. V. Zelevinsky) Discriminants of polynomials in several variables and triangulations of Newton polytopes, Leningrad Mathematical Journal, 2 (1991), 449--505.
  18. (with I. M. Gelfand, A. V. Zelevinsky) Newton polytopes of classical discriminant and resultant, Adv. in Math. 84 no. 2 (1990), 237--254.
  19. (with I. M. Gelfand, A. V. Zelevinsky) Generalized Euler integrals and A-hypergeometric functions, Adv. in Math. 84 no. 2 (1990), 255--271.
  20. (with V. A. Voevodsky) Free n-category generated by a cube, oriented matroids and higher Bruhat orders, Funct. Anal. and Appl. 25 (1991), 50--52.
  21. (with V. A. Voevodsky) Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders, Cah. Top. Geom. Diff. (1991), 11--27.
  22. (with V. A. Voevodsky) Infinity-groupoids and homotopy types, Cah. Top. Geom. Diff. 32 (1991), 29--46.
  23. (with A. I. Bondal) Enhanced triangulated categories. Mathematics of USSR - Sbornik 70 (1991), 93--107.
  24. A characterization of A-discriminantal hypersurfaces in terms of the logarithmic Gauss map, Mathematische Annalen, 290 (1991), 277--285.
  25. (with B. Sturmfels and A. Zelevinsky) Quotients of toric varieties, Math. Ann. 290 (1991), 643--655.
  26. (with B. Sturmfels and A. Zelevinsky) Chow polytopes and general resultants, Duke Math. J. 67 (1992), 189--218.
  27. (with I. Gelfand and A. Zelevinsky) Hyperdeterminants, Advances in Math. 96 (1992), 226--263.
  28. (with I. Gelfand and A. Zelevinsky) Hypergeometric functions, toric varieties and Newton polyhedra, in M. Kashiwara, T. Miwa (eds.) Special Functions, Springer-Verlag, 1992, 104--121.
  29. (with V. A. Voevodsky) 2-categories and Zamolodchikov's equations, Proc. Symp. Pure Math. 56 (1994), part 2, p. 177-259.
  30. Veronese curves and Grothendieck-Knudsen moduli space M(0,n), Journal of Algebraic Geometry, 2 (1993), 239--262.
  31. Chow quotient of Grassmannians I, Adv. Soviet Math. 16, part 2, p. 29-110.
  32. The permuto-associahedron, MacLane coherence theorem and the asymptotic zones for the KZ equation, Journal of Pure and Applied Algebra, 85 (1993), 119--142.
  33. (with V. Voevodsky) Braided monoidal 2-categories and Manin-Schechtman higher braid groups, J. Pure Appl. Algebra, 92 (1994), 241-267.
  34. (with I. Dolgachev) Arrangements of hyperplanes and vector bundles on the projective space, Duke Math. Journal, 71 (1993), 633-664.
  35. (with I.M. Gelfand) On the dimension and degree of the projective dual variety: a q-analog of the Katz-Kleiman formula, in: ``The Gelfand Mathematical Seminars 1990-92" (L. Corwin, I. Gelfand, J.Lepowsky Eds.), p.27-33, Birkhauser, Boston, 1993.
  36. (with I. Dolgachev) Schur quadrics, cubic surfaces and vector bundles on the projective plane, Asterisque, 218 111-144, Soc. Math. France, 1994.
  37. (with V. Ginzburg) Koszul duality for operads, Duke Math. Journal, 76 (1994), 203-273.
  38. (with I.M. Gelfand, A.V. Zelevinsky) Discriminants, Resultants and Multidimensional Determinants, Birkhauser, Boston, 1994. (Monograph, 515p.)
  39. (with L. Billera, B. Sturmfels), Cellular strings on polytopes, Proc. AMS, 122 (1994), 549-555.
  40. (with E. Getzler) Cyclic operads and cyclic homology, in: ``Geometry, Topology and Physics for R. Bott", ed. S.-T. Yau, p. 167-201, International Press, Cambridge MA, 1995.
  41. (with V. Ginzburg, E. Vasserot) Langlands reciprocity for algebraic surfaces, Int. Math. Research Notes, 2 (1995), 147-160.
  42. Analogies between the Langlands correspondence and topological quantum field theory, in: ``Functional analysis on the eve of 21st century" (S. Gindikin, J. Lepowsky, R. Wilson Eds.), vol. 1 (Progress in Math. v. 131), p. 119-151, Birkhauser, 1995.
  43. A higher-dimensional generalization of the Goss zeta function, J. Number theory, 50 (1995), 363-375.
  44. Eisenstein series and quantum affine algebras, J. Math. Sciences, 84 (1997), 1311-1360.
  45. (with V. Ginzburg, E. Vasserot) Residue construction of Hecke algebras, Advances in Math. 138 (1997), 1-19.
  46. (with E. Getzler) Modular operads, Compositio Math. 110 (1998), 65-126.
  47. Heisenberg doubles and derived categories, J. of Algebra, 22 (1998), 712-744.
  48. Hypergeometric functions on reductive groups, in ``Integrable systems and algebraic geometry" (M.H. Saito, Y. Shimizu, K. Yeno Eds.), p. 236-281, World Scientific Publ. 1998.
  49. Operads in algebraic geometry, in: Proceedings of the International Congress of Mathematicians (Berlin, 1998), vol. 2, p. 277-286, Deutsche Mathematische Vereinigung, 1998.
  50. Noncommutative geometry based on commutator expansions, J. reine und angew. Math. 505 (1998), 73-118.
  51. E. Getzler, M. Kapranov (Eds.) Higher Category Theory, Contemporary Math. 230, American Math. Soc. 1998. (Edited volume of proceedings).
  52. (with M. Saito) Hidden Stasheff polytopes in algebraic K-theory and in the space of Morse functions, Contemp. Math.. 227 (1999), 191-225.
  53. Rozansky-Witten invariants via Atiyah classes, Compositio Math. 115 (1999), 71-113.
  54. (with E. Vasserot) Kleinian singularities, derived categories and Hall algebras, Math. Ann. 316 (2000), 565-576.
  55. Injective resolutions of BG and the derived moduli space of local systems, J. Pure Appl. Alg. 155 (2001), 167-179.
  56. (with I.Ciocan-Fontanine) Derived Quot schemes, Ann. Sci. ENS 34 (2001), 403-440.
  57. (with J. Franecki) The Gauss map and a noncompact Riemann-Roch formula for constructible sheaves on semiabelian varieties, Duke Math. Journal 104 (2000), 171-180.
  58. Double affine Hecke algebras and 2-dimensional local fields, Journal of the AMS 14 (2001), 239-262.
  59. (with Y. Manin) Modules and Morita theory for operads, Amer. J. Math. to appear.