On divisorial filtrations on sheaves

Details On divisorial filtrations on sheaves On divisorial filtrations on sheaves

2005-02-17

arxiv.org/abs/math/0502368v1

Mathematics

Algebraic Geometry

Latex,14 pages

Scientific paper

A notion of Poincar\'e series was introduced by A.Campillo et al. It was developed by Delgado and Gusein-Zade for a multi-index filtration corresponding to the sequence of blow-ups. The present paper suggests the way to generalize the notion of Poincar\'e series to the case of arbitrary locally free sheaf on the modification of complex plane $\mathbb{C}^2$. This series is expressed through the topological invariants of the sheaf. For the sheaf of holomorphic functions the answer coincides with the Poincar\'e series found before.

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