SMS scnews item created by Bill Unger at Tue 14 Aug 2007 1217
Type: Seminar
Distribution: World
Expiry: 16 Aug 2007
Calendar1: 16 Aug 2007 1505-1600
CalLoc1: Carslaw 535

Computational Algebra Seminar: Beck -- Formal Desingularization of Surfaces in P^3

Speaker: Tobias Beck (RICAM)
Title: Formal Desingularization of Surfaces in P^3
Time & Place: 3:05-4pm, Thursday 16 August, Carslaw 535.

In algebraic geometry, theoretical arguments are often
based on the existence of smooth models. In practice, smooth
models may be computed using the constructive resolution
algorithms of Villamayor or Bierstone-Milman. But any algorithm
relying on a resolution then suffers from the high computational
complexity of those general algorithms.

In this talk we introduce formal desingularizations as a weak
version of resolutions. We also show how they can be computed
using the method of Jung-Abhyankar, a specialized resolution
procedure for surfaces. As an application, and an indication of
usefulness, we demonstrate how to compute the graded module
associated to the direct image of the canonical sheaf.

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