Abstract:The Hassett-Keel program seeks to offer a modular interpretation for the log minimal model program of the moduli space of stable curves. Alper, Fedorchuk, and Smyth have proposed a conjectural framework for this program by analyzing Gorenstein curve singularities under the action of G_m. Our work draws parallels between this approach and the study of the Kontsevich-Zorich conjectures ...
Abstract:For a del Pezzo surface of degree ≥ 3, we compute the oscillatory integral for its mirror Landau Ginzburg model in the sense of the Gross-Siebert program. We explicitly construct the mirror cycle of a line bundle and show that the leading order of the integral on this cycle involves the twisted Chern character and the Gamma class. It proves a mirror symmetric version of the Gamma con...