Preprint 2023-05
Gaëtan Borot, Maksim Karev, and Danilo Lewanski
ON ELSV-TYPE FORMULAE AND RELATIONS BETWEEN OMEGA-INTEGRALS VIA DEFORMATIONS OF SPECTRAL CURVES
Abstract: The general relation between Chekhov–Eynard–Orantin topological recursion and the intersection theory on the moduli space of curves, the deformation techniques in topological recursion, and the polynomiality dependency of its deformation parameters can be combined to derive vanishing relations involving intersection indices of tautological classes. We apply this strategy to three different families of spectral curves and show they give vanishing relations for integrals involving Omega-classes. The first class of vanishing relations are genus-independent and generalises the vanishings found by Johnson–Pandharipande–Tseng [JPT11] and by the authors jointly with Do and Moskovsky [BDK+22]. The two other class of vanishing relations are of a different nature and depend on the genus.
31 pp.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2023-05