On Divisorial Filtrations on Sheaves
نویسنده
چکیده
A notion of Poincaré series was introduced in [1]. It was developed in [2] for a multi-index filtration corresponding to the sequence of blow-ups. The present paper suggests the way to generalize the notion of Poincaré series to the case of arbitrary locally free sheaf on the modification of complex plane C 2. This series is expressed through the topological invariants of the sheaf. For the sheaf of holomorphic functions the answer coincides with the Poincaré series from [2].
منابع مشابه
Moduli Space of Principal Sheaves over Projective Varieties
Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a Riemann surface and constructed a projective moduli space of such objects. We generalize Ramanathan’s notion and construction to higher dimension, allowing also objects which we call semistable principal G-sheaves, in order to obtain a projective moduli space: a principal G-sheaf on a...
متن کاملResolutions and Cohomologies of Toric Sheaves. The affine case
We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of indecomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that the category of reflexive toric sheaves is equivalent to the category of vector spaces together with a certain family of filtrations. Within th...
متن کاملOn Gieseker stability for Higgs sheaves
We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective algebraic manifolds. In particular, we show that Gieseker stability for torsion-f...
متن کاملGeneric Vanishing Filtrations and Perverse Objects in Derived Categories of Coherent Sheaves
This is a partly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: generic vanishing in the context of vanishing theorems and birational geometry ([GL1], [GL2], [ClH], [Hac], [PP2], [PP4]), and perverse coherent sheaves in the context of derived categories ([Ka], [Be], [ABe], [YZ]). Criteria for checking either c...
متن کاملGraded Rings and Equivariant Sheaves on Toric Varieties
In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spaces. We systematically construct the theory from the point of view of graded ring theory and this way we consi...
متن کامل