Alexander Polischchuk (Uni Oregon)
Wednesday, May 23, 2018 - 13:00
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 1.114, 1. Stock
Forschungsseminar "Algebraische Geometrie"
Prof. Dr. Gavril Farkas, Prof. Dr. Bruno Klingler
In this talk I will discuss the moduli spaces of pointed curves with possibly non-nodal singularities such that the marked points form a nonspecial ample divisor. I will show that such curves have natural projective embeddings, with a canonical choice of homogeneous coordinates up to rescaling. Using Groebner bases technique this leads to the identification of the moduli stack with some global quotient by a torus action. Looking at the corresponding GIT quotients one gets birational projective models of Mg,n, some of which can be explicitly described. As another application, I will construct a birational morphism contracting the Weierstrass divisor in Mg,1 to a point.
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