Geometry & Topology

Counting lattice points in compactified moduli spaces of curves

Norman Do and Paul Norbury

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Abstract

We define and count lattice points in the moduli space ¯g,n of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space g,n. The enumeration produces polynomials whose top degree coefficients are tautological intersection numbers on ¯g,n and whose constant term is the orbifold Euler characteristic of ¯g,n. 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 ¯g,n.

Article information

Source
Geom. Topol., Volume 15, Number 4 (2011), 2321-2350.

Dates
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
https://projecteuclid.org/euclid.gt/1513732369

Digital Object Identifier
doi:10.2140/gt.2011.15.2321

Mathematical Reviews number (MathSciNet)
MR2862159

Zentralblatt MATH identifier
1236.32007

Subjects
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]

Keywords
moduli space stable maps Euler characteristic

Citation

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


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