Moduli spaces of curves with nonspecial divisors

Vortrag von Alexander Polishchuk

Datum: 09.04.18  Zeit: 13.15 - 14.45  Raum: Y27H25

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 with the quotient of an affine scheme by the torus action. These moduli spaces also have a natural interpretation in terms of the Krichever map. As an application, I will construct a birational morphism contracting the Weierstrass divisor in M_{g,1} to a point.