Geometry & Topology
- Geom. Topol.
- Volume 15, Number 4 (2011), 2321-2350.
Counting lattice points in compactified moduli spaces of curves
We define and count lattice points in the moduli space of stable genus curves with labeled points. This extends a construction of the second author for the uncompactified moduli space . The enumeration produces polynomials whose top degree coefficients are tautological intersection numbers on and whose constant term is the orbifold Euler characteristic of . We prove a recursive formula which can be used to effectively calculate these polynomials. One consequence of these results is a simple recursion relation for the orbifold Euler characteristic of .
Geom. Topol., Volume 15, Number 4 (2011), 2321-2350.
Received: 12 May 2011
Revised: 26 August 2011
Accepted: 23 September 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 14N10: Enumerative problems (combinatorial problems) 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Do, Norman; Norbury, Paul. Counting lattice points in compactified moduli spaces of curves. Geom. Topol. 15 (2011), no. 4, 2321--2350. doi:10.2140/gt.2011.15.2321. https://projecteuclid.org/euclid.gt/1513732369