2000 character limit reached
Refined sheaf counting on local K3 surfaces
Published 19 Mar 2024 in math.AG and hep-th | (2403.12741v1)
Abstract: We compute all refined sheaf counting invariants -- Vafa-Witten, reduced DT, stable pairs and Gopakumar-Vafa -- for all classes on local $K3$ surfaces. Along the way we develop rank 0 Vafa-Witten theory on $K3$ surfaces. An important feature of the calculation is that the ``instanton contribution" -- of sheaves supported scheme theoretically on $S$ -- to any of the invariants depends only on the square of the class, not its divisibility.
- S. Katz, A. Klemm and R. Pandharipande, with an Appendix by R. P. Thomas, On the motivic stable pairs invariants of K3𝐾3K3italic_K 3 surfaces, in “K3𝐾3K3italic_K 3 surfaces and their moduli”, eds. C. Faber, G. Farkas and G. van der Geer, Prog. in Math. 315 (2016), 111–146. arXiv:1407.3181.
- G. Oberdieck and R. Pandharipande, Curve counting on K3×E𝐾3𝐸K3\times Eitalic_K 3 × italic_E, the Igusa cusp form χ10subscript𝜒10\chi_{10}italic_χ start_POSTSUBSCRIPT 10 end_POSTSUBSCRIPT, and descendent integration, in “K3𝐾3K3italic_K 3 surfaces and their moduli”, eds. C. Faber, G. Farkas and G. van der Geer, Prog. in Math. 315 (2016), 245–278. arXiv:1411.1514.
- R. Pandharipande and R. P. Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009), 407–447. arXiv:0707.2348.
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