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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.
Toda, Yukinobu 1
@article{GT_2016_20_1_a10,
author = {Toda, Yukinobu},
title = {Stable pair invariants on {Calabi{\textendash}Yau} threefolds containing {\ensuremath{\mathbb{P}}2}},
journal = {Geometry & topology},
pages = {555--611},
publisher = {mathdoc},
volume = {20},
number = {1},
year = {2016},
doi = {10.2140/gt.2016.20.555},
url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2016.20.555/}
}
Toda, Yukinobu. Stable pair invariants on Calabi–Yau threefolds containing ℙ2. Geometry & topology, Tome 20 (2016) no. 1, pp. 555-611. doi : 10.2140/gt.2016.20.555. http://geodesic.mathdoc.fr/articles/10.2140/gt.2016.20.555/
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