Volume 15, issue 4 (2011)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Counting lattice points in compactified moduli spaces of curves

Norman Do and Paul Norbury

Geometry & Topology 15 (2011) 2321–2350

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.

moduli space, stable maps, Euler characteristic
Mathematical Subject Classification 2000
Primary: 32G15
Secondary: 14N10, 05A15
Received: 12 May 2011
Revised: 26 August 2011
Accepted: 23 September 2011
Published: 25 December 2011
Proposed: Jim Bryan
Seconded: Richard Thomas, Shigeyuki Morita
Norman Do
Department of Mathematics and Statistics
The University of Melbourne
Victoria 3010
Paul Norbury
Department of Mathematics and Statistics
The University of Melbourne
Victoria 3010