Gromov-Witten theory, Hurwitz numbers, and Matrix models, I

作者: Andrei Okounkov , Rahul Pandharipande

DOI:

关键词:

摘要: The main goal of the paper is to present a new approach via Hurwitz numbers Kontsevich's combinatorial/matrix model for intersection theory moduli space curves. A secondary an exposition circle ideas involved: numbers, Gromov-Witten projective line, matrix integrals, and random trees. Further topics will be treated in sequel.

参考文章(57)
D. Aldous, Stochastic Analysis: The Continuum random tree II: an overview Cambridge University Press. pp. 23- 70 ,(1991) , 10.1017/CBO9780511662980.003
R. Pandharipande, The Toda equations and the Gromov-Witten theory of the Riemann sphere arXiv: Algebraic Geometry. ,(1999)
R. P. Thomas, Derived categories for the working mathematician arXiv: Algebraic Geometry. ,(2000)
David Mumford, Towards an Enumerative Geometry of the Moduli Space of Curves Arithmetic and Geometry. pp. 271- 328 ,(1983) , 10.1007/978-1-4757-9286-7_12
Yuri I. Manin, Sergei I. Gelfand, Methods of Homological Algebra ,(1996)
Maxim Kontsevich, Enumeration of Rational Curves Via Torus Actions arXiv: High Energy Physics - Theory. pp. 335- 368 ,(1995) , 10.1007/978-1-4612-4264-2_12
Jun Li, Gang Tian, Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties Journal of the American Mathematical Society. ,vol. 11, pp. 119- 174 ,(1998) , 10.1090/S0894-0347-98-00250-1
V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity Physics Letters B. ,vol. 257, pp. 329- 334 ,(1991) , 10.1016/0370-2693(91)91901-7
A. Hurwitz, Ueber die Anzahl der Riemann'schen Flächen mit gegebenen Verzweigungspunkten. Mathematische Annalen. ,vol. 55, pp. 53- 66 ,(1901) , 10.1007/BF01448116
Maxim Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function Communications in Mathematical Physics. ,vol. 147, pp. 1- 23 ,(1992) , 10.1007/BF02099526