Description

Moduli spaces of curves (also known as Mg) and moduli spaces of K3 surfaces (Fg) are fundamental objects in modern Algebraic Geometry and many questions about the geometry of these spaces remain open. There is a beautiful connection between K3 surfaces and moduli spaces of curves in low genus explored in depth by Mukai in a long series of papers. This connection involves the classification of Fano varieties of low index, moduli of sheaves on curves and non abelian Brill-Noether theory among other ingredients. This connection has being extensively used to classify various moduli spaces, such as moduli spaces of spin curves and Prym curves using Nikulin surfaces, and strata of differentials among others. Depending on the interest we will decide on a sub-collection of this topics. The main goal is to get acquainted with questions about the birational geometry of moduli spaces, see examples and focus on open questions.

We meet on Friday's from 1.30pm to 2pm in 509/511 Lake Hall

Attention!! From Oct. 4th on we meet on Friday's from 11.30am to 2pm in 299 Ryder Hall

General References

• J. Harris and I. Morrison. Moduli of Curves. Grad. Texts in Math., Springer, 1998.

• E. Arbarello, M. Cornalba, and P. A. Griffiths. Geometry of algebraic curves. Vol. II, Grundlehren Math. Wiss., vol. 267. New York: Springer-Verlag, 2011.

• E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris. Geometry of algebraic curves. Vol. I, Grundlehren Math. Wiss., vol. 267. New York: Springer-Verlag, 1985.

• D. Huybrechts. Lectures on K3 Surfaces.Cambridge st. in adv. math., vol. 158, Cambridge University Press, 2016.