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.
Citation
Yukinobu Toda. "Stable pair invariants on Calabi–Yau threefolds containing $\mathbb{P}^2$." Geom. Topol. 20 (1) 555 - 611, 2016. https://doi.org/10.2140/gt.2016.20.555
Information