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Koszul duality for Operads

- V. Ginzburg, M. Kapranov
- Mathematics
- 1 October 1994

(0.1) The purpose of this paper is to relate two seemingly disparate developments. One is the theory of graph cohomology of Kontsevich [Kon 2 3] which arose out of earlier works of Penner [Pe] and… Expand

Discriminants, Resultants, and Multidimensional Determinants

- I. M. Gelʹfand, M. Kapranov, A. V. Zelevinsky
- Mathematics
- 1 March 1994

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General… Expand

ENHANCED TRIANGULATED CATEGORIES

- A. Bondal, M. Kapranov
- Mathematics
- 28 February 1991

A solution is given to the problem of describing a triangulated category generated by a finite number of objects. It requires the notion of "enhancement" of a triangulated category, by means of the… Expand

On the derived categories of coherent sheaves on some homogeneous spaces

- M. Kapranov
- Mathematics
- 1 October 1988

Rozansky–Witten invariants via Atiyah classes

- M. Kapranov
- MathematicsCompositio Mathematica
- 13 April 1997

Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of ‘weights’ (numbers, one for each trivalent graph) and used them to construct invariants of topological… Expand

Hypergeometric functions and toral manifolds

- I. Gel'fand, A. V. Zelevinskii, M. Kapranov
- Mathematics
- 1 April 1989

Cyclic Operads and Cyclic Homology

- E. Getzler, M. Kapranov
- Mathematics
- 1995

The cyclic homology of associative algebras was introduced by Connes [4] and Tsygan [22] in order to extend the classical theory of the Chern character to the non-commutative setting. Recently, there… Expand

Non-archimedean amoebas and tropical varieties

- M. Einsiedler, M. Kapranov, D. Lind
- Mathematics
- 23 August 2004

Abstract We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For… Expand

Kleinian singularities, derived categories and Hall algebras

- M. Kapranov, E. Vasserot
- Mathematics
- 2 December 1998

We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the… Expand

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