Geodesic
On divisorial filtrations on sheaves
Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 825-837

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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. 
@article{MZM_2006_79_6_a1,
     author = {E. A. Gorskii},
     title = {On divisorial filtrations on sheaves},
     journal = {Matemati\v{c}eskie zametki},
     pages = {825--837},
     publisher = {mathdoc},
     volume = {79},
     number = {6},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a1/}
}
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E. A. Gorskii. On divisorial filtrations on sheaves. Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 825-837. http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a1/