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arXiv · 2309.03673

Semistable refined Vafa-Witten invariants

Henry Liu
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Abstract

For any smooth complex projective surface $S$, we construct semistable refined Vafa-Witten invariants of $S$ 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.

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Henry Liu. 2023-09-07. Semistable refined Vafa-Witten invariants. https://arxiv.org/abs/2309.03673

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