7 research outputs found
Rank-one sheaves and stable pairs on surfaces
We study rank-one sheaves and stable pairs on a smooth projective complex
surface. We obtain an embedding of the moduli space of limit stable pairs into
a smooth space. The embedding induces a perfect obstruction theory, which, over
a surface with irregularity 0, agrees with the usual deformation-obstruction
theory. The perfect obstruction theory defines a virtual fundamental class on
the moduli space. Using the embedding, we show that the virtual class equals
the Euler class of a vector bundle on the smooth ambient space. As an
application, we show that on , the expected count of the finite
Quot scheme in arXiv:1610.04185 is its actual length. We also obtain a
universality result for tautological integrals on the moduli space of stable
pairs.Comment: 29 pages. In this new version, we extend one of our main theorems to
more cases. Hence, we have changed the title. We also fix a mistake in
Proposition 7.2 and one in the proof of Proposition 4.1 in the first version.
Comments are welcome
Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions
Given a (projective) conifold transition of smooth projective threefolds from
to , we show that if the Gromov--Witten/Pandharipande--Thomas descendent
correspondence holds for the resolution , then it also holds for the
smoothing with stationary descendent insertions. As applications, we show
the correspondence in new cases.Comment: 23 pages. Comments are welcome