Quantum Intersection Rings

Di Francesco, P. ; Itzykson, C.

Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 46 (1994), p. 153-226 / Harvested from Numdam

Détail

Publié le : 1994-01-01

Bibliographie

[1] E. Witten, Two dimensional gravity and intersection theory on moduli space, Surv. in Diff. Geom. 1 (1991) 243-310. | MR 1144529 | Zbl 0757.53049

[2] R. Dijkgraaf, H. Verlinde and E. Verlinde, Topological strings in $d < 1$, Nucl. Phys. B352 (1991) 59-86.

[3] M. Kontsevich and Y. Manin, Gromov-Witten classes, quantum cohomology and enumerative geometry, preprint MPI-94-21. | MR 1291244 | Zbl 0853.14020

[4] B. Dubrovin, Integrable systems in topological field theory, Nucl. Phys. B379 (1992) 627; Geometry of 2D topological field theories, preprint SISSA-89/94/FM. | MR 1175565

[5] C. Itzykson, Counting rational curves on rational surfaces, Int. J. of Mod. Phys. A to appear. | Zbl 0885.14027

[6] H. Schubert, Kalkül der abzählenden Geometrie, reprint, Springer, New York (1979). | MR 555576 | Zbl 0417.51008

[7] I. Vainsencher, Enumeration of n-fold tangent hyperplanes to a surface, Journal of Algebraic Geometry, to appear. | MR 1325790 | Zbl 0928.14035

[8] S. Kleiman and R. Piene, private communication.

[9] J. Semple and L. Roth, Introduction to algebraic geometry, Clarendon Press, Oxford (1987). | MR 814690 | Zbl 0041.27903

[10] R. Piene, On the enumeration of algebraic curves- from circles to instantons, to appear in the Proceedings of the first European Congress of Mathematics, Paris, 1992(Birkhäuser). | MR 1341850 | Zbl 0835.14021

[11] J. Harris, Algebraic geometry-a first course, Springer, New York (1992). | MR 1182558 | Zbl 0779.14001

[12] Y. Manin, Cubic forms: algebra, geometry, arithmetics, North Holland, Amsterdam (1974). | MR 833513 | Zbl 0277.14014

[13] E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, IASSNS preprint. | MR 1358625 | Zbl 0863.53054

[14] I. Macdonald, Notes on Schubert polynomials, LACIM, Université du Québec à Montréal (1991). | MR 1161461

[15] J. Harris, Galois groups of enumerative problems, Duke Math. Journ. 46 (1979) 685-724. | MR 552521 | Zbl 0433.14040

[16] M. Kontsevich Intersection theory on the moduli space of curves and matrix Airy function, Comm. Math. Phys. 147 (1992) 1. | MR 1171758 | Zbl 0756.35081

[17] C. Itzykson and J.-B. Zuber, Combinatorics of the modular group II, Int. Jour. Mod. Phys. A7 (1992) 5661. | MR 1180858 | Zbl 0972.14500

[18] A. Fokas and M. Ablowitz, On a unified approach to transformations and elementary solutions of Painlevé equations, J. Math. Phys. 23 (1982) 2033; | MR 679998 | Zbl 0504.34022

A. Fokas and Y. Yortsos, The transformation properties of the sixth Painlevé equation and one-parameter families of solutions, Lett. Nuovo Cimento 30 (1981) 539-544; | MR 621591

A. Fokas, R. Leo, L. Martina and G. Soliani, The scaling reduction of the three-wave resonant system and the Painlevé VI equation, Phys. Lett. A115 (1986) 329. | MR 838679