Moduli of Stable Curves and Stable Maps
Student No.:40
Time:13:30-15:05,2017.10.9/ 10.11/ 10.13/ 10.23/ 10.25/ 10.27
Instructor:Chiu-Chu Melissa Liu  [Columbia University]
Place:Conference Room 3, Floor 2, Jinchunyuan West Building
Starting Date:2017-9-11
Ending Date:2017-10-27


This course is an introduction to moduli of stable curves, moduli of stable maps, and Gromov-Witten theory. Topics include: moduli spaces of stable curves, cohomology and the Picard group of moduli of stable curves, moduli spaces of stable maps, perfect obstruction theory and virtual fundamental classes, Gromov-Witten invariants, quantum cohomology, virtual localization.



Basic knowledge of algebraic geometry and algebraic topology.



1)      E. Arbarello, M. Coralba, P. Griffiths, Geometry of Algebraic Curves

2)      K. Behrend, Y. Manin, “Stacks of stable maps and Gromov-Witten invariants, “Duke Math. J. 85 (1996) 1-60.

3)      W. Fulton and R. Pandharipande, “Notes on stable maps and quantum cohomology,”Algebraic geometr--Santa Cruz 1995, 45--96, Proc. Sympos. Pure Math, 62, Part 2, Amer. Math. Soc., Providence, RI, 1997.

4)      K. Behrend, B. Fantechi, “The intrinsic normal cone,” Invent. Math. 128 (1997), no. 1, 45-88.

5)      K. Behrend, “Gromov-Witten invariants in algebraic geometry.” Invent. Math. 127 (1997), no. 3, 601-607.

6)      T. Graber. R. Pandharipande, “Localization of virtual classes,” Invent. Math. 135 (1999) no. 2, 487-518.