List of Publications: Mikhail Kapranov
- The derived category of coherent sheaves on Grassmann varieties,
Functional Analysis and Applications 17 (1983), 145--146.
- On the derived category of coherent sheaves on Grassmann varieties,
Mathematics of USSR - Izvestija, 24 (1985), 183--192.
- (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.
- The derived category of coherent sheaves on a quadric,
Funct. Anal. and Appl. 20 (1986), 141--142.
- On cuspidal divisors on modular varieties of elliptic modules,
Math. USSR
Izv. 30 (1988), 533--547.
- On the derived category and K-functor of coherent sheaves on
intersections of quadrics, Math. USSR Izv. 32 (1989), 191--204.
- On the derived categories of coherent sheaves on some homogeneous
spaces, Inventiones Mathematicae 92 (1988), 479--508.
- (with I. M. Gelfand, A. V. Zelevinsky) Equations of hypergeometric
type and Newton polytopes, Soviet Mathematics -- Doklady, 37
(1988), 678--683].
- (with I. M. Gelfand, A. V. Zelevinsky) Hypergeometric functions
and toric varieties, Funct. Anal. and Appl. 23
no. 2 (1989),
12--26.
- (with I. M. Gelfand, A. V. Zelevinsky) A-discriminants and
Cayley-Koszul complexes, Sov. Math. Dokl. 40 (1990), 239--243.
- (with A. I. Bondal) Representable functors, Serre functors and
mutations, Math. USSR Izvestija, 35 (1990), 519--541.
- (with I. M. Gelfand, A. V. Zelevinsky) Projectively dual
varieties and hyperdeterminants,
Sov. Math. Dokl. 39 no. 2 (1989), 385--389.
- (with I. M. Gelfand, A. V. Zelevinsky) Newton polyhedra of
principal A-determinants, Soviet Math. Dokl.
40 (1990),
278--281.
- On non-holonomic D-modules and non-constructible perverse
sheaves, Funct. Anal. and Appl. 23 (1989), 325--326.
- (with I. M. Gelfand, A. V. Zelevinsky) On discriminants of
polynomials in several variables, Funct. Anal. and Appl. 24
no. 1 (1990), 1--4.
- Mutations and Serre functors in constructible sheaves,
Funct. Anal. and Appl. 24 (1990), 155--156.
- (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.
- (with I. M. Gelfand, A. V. Zelevinsky) Newton polytopes of
classical discriminant and resultant, Adv. in Math. 84 no. 2
(1990), 237--254.
- (with I. M. Gelfand, A. V. Zelevinsky) Generalized Euler
integrals and A-hypergeometric functions, Adv. in Math. 84
no. 2 (1990), 255--271.
- (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.
- (with V. A. Voevodsky) Combinatorial-geometric aspects of
polycategory theory: pasting schemes and higher Bruhat orders, Cah.
Top. Geom. Diff. (1991), 11--27.
- (with V. A. Voevodsky) Infinity-groupoids and homotopy types,
Cah. Top. Geom. Diff. 32 (1991), 29--46.
- (with A. I. Bondal) Enhanced triangulated categories.
Mathematics of USSR - Sbornik 70 (1991), 93--107.
- A characterization of A-discriminantal hypersurfaces in terms
of the logarithmic Gauss map, Mathematische Annalen,
290 (1991),
277--285.
- (with B. Sturmfels and A. Zelevinsky) Quotients of toric
varieties, Math. Ann. 290 (1991), 643--655.
- (with B. Sturmfels and A. Zelevinsky) Chow polytopes and general
resultants, Duke Math. J. 67 (1992), 189--218.
- (with I. Gelfand and A. Zelevinsky) Hyperdeterminants,
Advances in Math. 96 (1992), 226--263.
- (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.
- (with V. A. Voevodsky) 2-categories and Zamolodchikov's
equations, Proc. Symp. Pure Math. 56 (1994), part 2, p. 177-259.
- Veronese curves and Grothendieck-Knudsen moduli space
M(0,n), Journal of Algebraic Geometry,
2 (1993), 239--262.
- Chow quotient of Grassmannians I, Adv. Soviet
Math. 16, part 2, p. 29-110.
- The permuto-associahedron, MacLane coherence theorem and the
asymptotic zones for the KZ equation, Journal of Pure
and Applied
Algebra, 85 (1993), 119--142.
- (with V. Voevodsky) Braided monoidal 2-categories and
Manin-Schechtman higher braid groups,
J. Pure Appl. Algebra, 92 (1994), 241-267.
- (with I. Dolgachev) Arrangements of hyperplanes and vector
bundles on the projective space, Duke Math. Journal,
71 (1993),
633-664.
- (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.
- (with I. Dolgachev) Schur quadrics, cubic surfaces and
vector bundles on the projective plane, Asterisque,
218
111-144, Soc. Math.
France, 1994.
- (with V. Ginzburg) Koszul duality for operads,
Duke Math. Journal, 76 (1994), 203-273.
- (with I.M. Gelfand, A.V. Zelevinsky) Discriminants,
Resultants and Multidimensional Determinants, Birkhauser, Boston,
1994. (Monograph, 515p.)
- (with L. Billera, B. Sturmfels), Cellular strings on polytopes,
Proc. AMS, 122 (1994), 549-555.
- (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.
- (with V. Ginzburg, E. Vasserot) Langlands reciprocity for
algebraic surfaces, Int. Math. Research Notes,
2 (1995), 147-160.
- 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.
- A higher-dimensional generalization of the Goss zeta
function, J. Number theory, 50 (1995), 363-375.
- Eisenstein series and quantum affine algebras,
J. Math. Sciences, 84 (1997), 1311-1360.
- (with V. Ginzburg, E. Vasserot) Residue construction of Hecke algebras,
Advances in Math. 138 (1997), 1-19.
- (with E. Getzler) Modular
operads, Compositio Math.
110 (1998), 65-126.
- Heisenberg doubles and derived categories,
J. of Algebra, 22 (1998), 712-744.
- 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.
- Operads in algebraic geometry, in: Proceedings of the
International Congress
of Mathematicians (Berlin, 1998), vol. 2, p. 277-286,
Deutsche Mathematische Vereinigung, 1998.
- Noncommutative geometry based on commutator expansions,
J. reine und
angew. Math. 505 (1998), 73-118.
- E. Getzler, M. Kapranov (Eds.) Higher Category Theory,
Contemporary Math. 230, American Math. Soc. 1998.
(Edited volume of proceedings).
- (with M. Saito) Hidden Stasheff polytopes in algebraic
K-theory and in the space of Morse functions,
Contemp. Math.. 227 (1999), 191-225.
-
Rozansky-Witten invariants via Atiyah classes,
Compositio Math. 115 (1999), 71-113.
- (with E. Vasserot) Kleinian singularities, derived categories
and Hall algebras, Math. Ann. 316 (2000), 565-576.
- Injective resolutions of BG and the derived moduli space of local
systems, J. Pure Appl. Alg. 155 (2001), 167-179.
- (with I.Ciocan-Fontanine)
Derived Quot schemes,
Ann. Sci. ENS 34 (2001), 403-440.
- (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.
- Double affine Hecke algebras and 2-dimensional local fields, Journal of the AMS
14 (2001), 239-262.
- (with Y. Manin)
Modules and Morita theory for operads, Amer. J. Math.
to appear.