Semistable refined Vafa-Witten invariants
Algebraic Geometry
2025-12-30 v3
Abstract
For any smooth complex projective surface , we construct semistable refined Vafa-Witten invariants of which prove the main conjecture of arXiv:1810.00078. This is done by extending part of Joyce's universal wall-crossing formalism to equivariant K-theory, and to moduli stacks with symmetric obstruction theories, particularly moduli stacks of sheaves on Calabi-Yau threefolds. An important technical tool which we introduce is the symmetrized pullback, along smooth morphisms, of symmetric obstruction theories.
Cite
@article{arxiv.2309.03673,
title = {Semistable refined Vafa-Witten invariants},
author = {Henry Liu},
journal= {arXiv preprint arXiv:2309.03673},
year = {2025}
}
Comments
33 pages. v3: the nonzero H1 case of the main theorem has been weakened due to a mistake in previous versions, plus minor revisions based on referee comments. Journal version