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.

Abstract:
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.