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Hodge-type integrals on moduli spaces of admissible covers

Renzo Cavalieri

Geometry & Topology Monographs 8 (2006) 167–194

DOI: 10.2140/gtm.2006.8.167

arXiv: math.AG/0411500

Abstract

In this paper we study a natural class of intersection numbers on moduli spaces of degree d admissible covers from genus g curves to P1, using techniques of localization. These intersection numbers involve tautological λ and ψ classes, and are in some sense analogous to Hodge Integrals on moduli spaces of stable curves.

We compute explicitly these numbers for all genera in degrees 2 and 3 and express the result in generating function form; we provide a conjecture for the general degree d case.

Keywords

Mathematical Subject Classification

Primary: 14C30

Secondary: 32S25, 58A14

References
Publication

Received: 9 March 2005
Accepted: 10 March 2005
Published: 21 September 2007

Authors
Renzo Cavalieri
Department of Mathematics
University of Utah
155 South 1400 East
Salt Lake City UT 84112
USA
Department of Mathematics
University of Michigan
2074 East Hall
530 Church Street
Ann Arbor MI 48109-1043
USA