Geometry & Topology

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

Yukinobu Toda

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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.

Article information

Geom. Topol., Volume 20, Number 1 (2016), 555-611.

Received: 19 November 2014
Revised: 13 April 2015
Accepted: 5 June 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 18E30: Derived categories, triangulated categories

stable pair invariants derived categories wall-crossing


Toda, Yukinobu. Stable pair invariants on Calabi–Yau threefolds containing $\mathbb{P}^2$. Geom. Topol. 20 (2016), no. 1, 555--611. doi:10.2140/gt.2016.20.555.

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