The 3-fold vertex via stable pairs
type: Item
instance of: scholarly article
title: The 3-fold vertex via stable pairs
zbMATH Open document ID: 1195.14073
author: Richard P. Thomas
author: Rahul Pandharipande
published in: Geometry \& Topology
publication date: 2009-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/0709.3823
review text: Donaldson-Thomas invariants, which count stable sheaves on projective threefolds, are important invariants, especially for Calabi-Yau threefolds. They are conjecturally equivalent to Gromov-Witten invariants of all genera on Calabi-Yau threefolds. In order to take away the contribution from embedded points inside curves in Calabi-Yau threefolds, we need to normalize the Donaldson-Thomas invariant. Pandharipande and Thomas found a more effective way that should capture these normalized Donaldson-Thomas invariant. Instead they count the number of stable pairs \([O_{X}\overset {s} \rightarrow F ]\) in a threefold \(X\). Here \(F\) is a pure sheaf supported on a curve in \(X\) and the cokernel of \(s\) has zero dimensional support. In this article, the authors compute these invariants via the localization method when \(X\) is toric. In the toric Calabi-Yau case, they are expressed in terms of pure box counting.
reviewed by: Naichung Conan Leung
Mathematics Subject Classification ID: 14N35
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 5553982
zbMATH Keywords: curve
zbMATH Keywords: threefold
zbMATH Keywords: Gromov-Witten
zbMATH Keywords: toric
MaRDI profile type: Publication
OpenAlex ID: W2016200805
arXiv ID: 0709.3823
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DOI: 10.2140/GT.2009.13.1835
description: scientific article