Intersection theory on the moduli space of curves. (English. Russian original) Zbl 0742.14021
Funct. Anal. Appl. 25, No. 2, 123-129 (1991); translation from Funkts. Anal. Prilozh. 25, No. 2, 50-57 (1991).
The paper gives a combinatorial method for the computation of the intersection indices of divisors on the moduli space of pointed algebraic curves. The corresponding generation function is the logarithmic statistical sum associated with some matrix model. According to the Witten hypothesis this statistical sum has to be a \(\tau\)-function for the Korteweg-de Vries hierarchy.
Reviewer: V.Z.Enol’skij (Kiev)
MSC:
| 14H10 | Families, moduli of curves (algebraic) |
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
intersection indices of divisors; moduli space of pointed algebraic curves; statistical sum; Korteweg-de Vries hierarchyReferences:
| [1] | E. Witten, ”Two-dimensional gravity and intersection theory of moduli space,” Princeton IAS preprint 90/45 (1990). |
| [2] | G. Segal and G. Wilson, ”Loop groups and equations of KdV type,” Inst. Hautes Études Sci. Publ. Math.,61, 5-65 (1985). · Zbl 0592.35112 · doi:10.1007/BF02698802 |
| [3] | D. Mumford, ”Towards an enumerative geometry of the moduli spaces of curves,” in: Arithmetic and Geometry, M. Artin and J. Tate (eds.), Birkhäuser, Boston (1983). · Zbl 0554.14008 |
| [4] | K. Strebel, Quadratic Differentials, Springer, Berlin (1984). |
| [5] | H. Sonoda and B. Zwiebach, ”Closed string field theory loops with symmetric factorizable quadratic differentials,” Nucl. Phys.,B331, 592-628 (1990). · doi:10.1016/0550-3213(90)90086-S |
| [6] | D. Bessis, C. Itzykson, and J.-B. Zuber, ”Quantum field theory techniques in graphical enumeration,” Adv. Appl. Math.,1, 109-157 (1980). · Zbl 0453.05035 · doi:10.1016/0196-8858(80)90008-1 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
