Program
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

Description: 

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.

 

Prerequisite: 

Basic knowledge of algebraic geometry and algebraic topology.

 

Reference:

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.