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Koszul duality for Operads
(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
Discriminants, Resultants, and Multidimensional Determinants
Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General
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
Rozansky–Witten invariants via Atiyah classes
  • M. Kapranov
  • Mathematics
    Compositio 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
Cyclic Operads and Cyclic Homology
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
Non-archimedean amoebas and tropical varieties
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
Kleinian singularities, derived categories and Hall algebras
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