Abstract:
The lectures will cover two main themes concerning the geometry
of the moduli space of curves: (1) Birational geometry of M_g, with
emphasis on the study of the cone of effective divisors, minimal models,
slopes and singularities of the moduli space and (2) properties of the
tautological intersection ring of M_g.
Suggested reading:
General references for M_g:
1) Harris, Morrison: Moduli of curves, Springer.
2) Arbarello, Cornalba, Griffiths: The geometry of algebraic curves, Vol. 2,
Springer.
More specific references:
3) Farkas: Aspects of the birational geometry of M_g, Surveys in
Differential Geometry Vol. 14 (2010), arXiv:0810.0702.
4) Farkas: Koszul divisors on moduli spaces of curves, American J. Math.
2009.
5) Faber: A conjectural description of the tautological ring of the moduli
space of curves, arXiv:math/9711218.