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Descendents on local curves: rationality

Part of:Projective and enumerative geometryFamilies, fibrations

Published online by Cambridge University Press:  01 November 2012

R. Pandharipande and
A. Pixton
R. Pandharipande
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA (email: rahulp@math.princeton.edu, rahul@math.ethz.ch)
A. Pixton
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA (email: apixton@math.princeton.edu)
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Abstract

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We study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geometry (equivariant with respect to the scaling 2-torus), including relative conditions and odd-degree insertions for higher-genus curves. The capped 1-leg descendent vertex (equivariant with respect to the 3-torus) is also proven to be rational. The results are obtained by combining geometric constraints with a detailed analysis of the poles of the descendent vertex.

Keywords

Donaldson–Thomasdescendentmodulisheaf

MSC classification

Secondary:14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants14D20: Algebraic moduli problems, moduli of vector bundles

Information

Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 1 , January 2013, pp. 81 - 124
Copyright
Copyright © The Author(s) 2012

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