The moduli space of curves as a stack, I
10:30:00 - 12:00:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)
In these two talks, we will introduce the proof of the groupoid of stable, n-pointed, genus g curves as a Deligne-Mumford stack in three stages. First, as a quotient groupoid, we show that it is isomorphic to the Hilbert scheme of v-log-canonically embedded, stable, n-pointed genus g curves quotient the projective general linear group. Then we briefly recall the Grothendieck's descent theory for quasi-coherent sheaves and use it to show that the moduli groupoid is a stack and, finally, Deligne-Mumford stack.
Reference: Arbarello, Cornalba, Griffiths: Geometry of Algebraic Curves, vol 2, chap 12.