The Hurwitz enumeration problem of branched covers and Hodge integrals

DOI10.1016/j.geomphys.2003.11.003zbMath1077.14078arXivhep-th/0009129OpenAlexW2118716145MaRDI QIDQ1781417

Yun S. Song, Stefano Monni, Jun S. Song

Publication date: 27 June 2005

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0009129

zbMATH Keywords

generating functionsHurwitz numbersdescendant Gromov-Witten invariants

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

Related Items

Explicit computation of some families of Hurwitz numbers ⋮ Realizations of certain odd-degree surface branch data ⋮ On the existence of branched coverings between surfaces with prescribed branch data. I ⋮ Explicit computation of some families of Hurwitz numbers. II ⋮ Quadratic recursion relations of Hodge intervals via localization ⋮ Branched covers of the sphere and the prime-degree conjecture ⋮ Two-dimensional Yang-Mills theory and moduli spaces of holomorphic differentials ⋮ Spherical conic metrics and realizability of branched covers ⋮ Surface branched covers and geometric 2-orbifolds ⋮ The Hurwitz existence problem for surface branched covers

Cites Work

• Nonequivalent coverings of Riemann surfaces with a prescribed ramification type
• A conjectural generating function for numbers of curves on surfaces
• Hurwitz numbers and intersections on moduli spaces of curves.
• The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
• Hodge integrals and Gromov-Witten theory
• Two-dimensional QCD as a string theory
• Branched coverings of riemann surfaces whose branch orders coincide with the multiplicity
• Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians
• The number of ramified covering of a Riemann surface by Riemann surface
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