Volume 20, issue 1 (2016)

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Stable pair invariants on Calabi–Yau threefolds containing $\mathbb{P}^2$

Yukinobu Toda

Geometry & Topology 20 (2016) 555–611
Abstract

We relate Pandharipande–Thomas stable pair invariants on Calabi–Yau 3–folds containing the projective plane with those on the derived equivalent orbifolds via the wall-crossing method. The difference is described by generalized Donaldson–Thomas invariants counting semistable sheaves on the local projective plane, whose generating series form theta-type series for indefinite lattices. Our result also derives non-trivial constraints among stable pair invariants on such Calabi–Yau 3–folds caused by a Seidel–Thomas twist.

Keywords
stable pair invariants, derived categories, wall-crossing
Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 18E30
References
Publication
Received: 19 November 2014
Revised: 13 April 2015
Accepted: 5 June 2015
Published: 29 February 2016
Proposed: Richard Thomas
Seconded: Jim Bryan, Yasha Eliashberg
Authors
Yukinobu Toda
Kavli Institute for the Physics and Mathematics of the Universe
University of Tokyo
5-1-5 Kashiwanoha, Kashiwa, Chiba
Kashiwa 277-8583
Japan