Journal of the Mathematical Society of Japan

Descendent theory for stable pairs on toric 3-folds

Rahul PANDHARIPANDE and Aaron PIXTON

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Abstract

We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg case. As a consequence, we prove the rationality of the relative stable pairs partition functions for all log Calabi-Yau geometries of the form $(X,K3)$ where $X$ is a nonsingular toric 3-fold.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1337-1372.

Dates
First available in Project Euclid: 24 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1382620196

Digital Object Identifier
doi:10.2969/jmsj/06541337

Mathematical Reviews number (MathSciNet)
MR3127827

Zentralblatt MATH identifier
1285.14061

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Keywords
enumerative geometry sheaves stable pairs descendents

Citation

PANDHARIPANDE, Rahul; PIXTON, Aaron. Descendent theory for stable pairs on toric 3-folds. J. Math. Soc. Japan 65 (2013), no. 4, 1337--1372. doi:10.2969/jmsj/06541337. https://projecteuclid.org/euclid.jmsj/1382620196


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