On divisorial filtrations on sheaves

E. A. Gorskii

M. V. Lomonosov Moscow State University

Abstract: In this paper, we generalize the notion of Poincaré series of a multi-index divisorial filtration corresponding to a collection of sigma-processes to the case of an arbitrary locally-free sheaf on the space of blow-ups of the complex plane $\mathbb C^2$. For an arbitrary sheaf, we establish a representation of the series in terms of topological invariants of the sheaf. In particular, for the sheaf of functions, this representation coincides with the Poincaré series obtained by Gusein-Zade and Delgado.

UDC: 512.6

Received: 14.02.2005
Revised: 07.10.2005

DOI: 10.4213/mzm2757

 English version: Mathematical Notes, 2006, 79:5, 771–782

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