The moduli space of curves as a stack, II


You-Cheng Chou ( National Taiwan University )
2017-03-06  15:30 - 18:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

This is the second talk of a series of two talks, where 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 Grothendieckกฆs 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.