Vertical Vafa–Witten invariants

Autores: Ties Laarakker
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 4, 2021
Idioma: inglés
DOI: 10.1007/s00029-021-00678-7
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Resumen
- We show that vertical contributions to (possibly semistable) Tanaka–Thomas–Vafa–Witten invariants are well defined for surfaces with pg(S)>0, partially proving conjectures of Tanaka and Thomas (Pure Appl Math Q 13:517–562, 2017) and Thomas (Commun Math Phys 378(2):1451–1500, 2020). Moreover, we show that such contributions are computed by the same tautological integrals as in the stable case, which we studied in Laarakker (Geom Topol 24(6):2781–2828, 2020). Using the work of Kiem and Li, we show that stability of universal families of vertical Joyce–Song pairs is controlled by cosections of the obstruction sheaves of such families.