Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Tuesday, July 20, 16:40 ~ 17:20 UTC-3

Effective cone of the moduli space of sheaves on the plane via minimal free resolutions

César Lozano Huerta

UNAM, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The minimal free resolution of a sheaf is a complex whose factors are sums of line bundles. On the other hand, the generalized Gaeta resolution of a general sheaf on the plane is a complex whose factors are non-trivial vector bundles of higher rank.

In this talk I will discuss the relation between these two resolutions and a dictionary between them. This dictionary recovers the effective cone of the moduli space of sheaves on the plane, and based on it, we propose an elementary algorithm to compute the stable base locus decomposition of the Hilbert scheme of points on the plane. We prove that this algorithm is correct in some cases.

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