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Counting lattice points
in compactified moduli spaces of curves
Norman Do and Paul Norbury |
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Geometry & Topology 15 (2011) 2321–2350
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Abstract |
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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 . |
Keywords
moduli space, stable maps, Euler characteristic
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Mathematical Subject Classification 2000
Primary: 32G15
Secondary: 14N10, 05A15
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References |
Publication
Received: 12 May 2011
Revised: 26 August 2011
Accepted: 23 September 2011
Published: 25 December 2011
Proposed: Jim Bryan
Seconded: Richard Thomas, Shigeyuki Morita
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Authors |
| Norman Do | |
| Department of Mathematics and
Statistics The University of Melbourne Victoria 3010 Australia |
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| http://www.ms.unimelb.edu.au/~nndo/ | |
| Paul Norbury | |
| Department of Mathematics and
Statistics The University of Melbourne Victoria 3010 Australia |
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| http://www.ms.unimelb.edu.au/~pnorbury/ | |
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