Birational Geometry of Moduli Spaces
Lecture notes and exercises (pdf).
These will be revised frequently in the next few weeks as people point out typos and mistakes. Please e-mail me any errors you spot or suggestions you have.
Books:
- Joe Harris and Ian Morrison, Moduli of Curves, Graduate Texts in Mathematics 187, Springer 1998.
- Robert Lazarsfeld, Positivity in Algebraic Geometry, Volumes I and II, Springer-Verlag, 2004
Papers:
- Dawei Chen and Izzet Coskun, Towards Mori's program for the moduli space of stable maps (with an appendix by Charley Crissman), (pdf).
- Dawei Chen and Izzet Coskun, Stable base locus decompositions of Kontsevich moduli spaces, (pdf).
- Izzet Coskun, Joe Harris and Jason Starr, The effective cone of the Kontsevich moduli space, (pdf).
Canadian Mathematical Bulletin. vol. 51 no. 4 (2008), pages 519-534.
- Izzet Coskun, Joe Harris and Jason Starr, The ample cone of the Kontsevich moduli space, (pdf).
Canadian Journal of Mathematics. vol. 61 no. 1 (2009), pages 109-123.
- Izzet Coskun and Jason Starr, Divisors on the space of maps to Grassmannians, (pdf).
International Mathematics Research Notices, vol. 2006, Article ID 35273, 25 pages, 2006.
- D. Eisenbud and J. Harris. Limit linear series: basic theory.
Invent. Math. 85(1986),
337-371.
- D. Eisenbud and J. Harris. The Kodaira dimension of the moduli space of curves of genus $\geq 23$.
Invent. Math. 90 (1987), no. 2, 359-387.
- William Fulton and Rahul Pandharipande, Notes on stable maps and quantum cohomology,
(pdf)
Algebraic geometry---Santa Cruz 1995, 45--96,
Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997.
- Angela Gibney, Sean Keel and Ian Morrison. Towards the ample cone of the moduli space of curves, (pdf)
J. Amer. Math. Soc. 15 (2002), no. 2, 273--294
- Joe Harris and David Mumford. On the Kodaira dimension of the moduli space of curves.
Invent. Math. 67(1982), 23-88.
- Brendan Hassett and Donghoon Hyeon, Log minimal model program for the moduli space of curves: The first flip, (pdf)
- Brendan Hassett and Donghoon Hyeon, Log canonical models for the moduli space of curves: The first divisorial contraction, (pdf)
Trans. Amer. Math. Soc. 361 (2009), no. 8, 4471--4489.
- Brendan Hassett and Yuri Tschinkel, On the effective cone of the moduli space of pointed rational curves, (ps)
Topology and geometry: commemorating SISTAG, 83--96, Contemp. Math., 314, Amer. Math. Soc., Providence, RI, 2002.
- Sean Keel and James McKernan, Contractible extremal rays on the moduli space of n-pointed genus-zero curves (pdf)