Laboratoire Angevin de Recherche en Mathématiques

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

We consider the non-selfadjoint, semiclassical Schrödinger operator \mathscr{L}(h) := -h^{2}\partial_{x}^{2}+e^{i\alpha}V , where \alpha \in (-\pi,\pi) and V\colon \R\to \R_{+} is even and vanishes at exactly two (symmetric) non-degenerate minima. We establish a semiclassical tun...

Twisted Kodaira–Spencer Classes and the Inequality of Severi †

Let X be a smooth minimal complex surface of general type subject to the inequality KX2<4χ(OX). The old problem of Severi states that the image of the Albanese map of such a surface is at most a curve. The problem was completely settled by Rita Pardini using the works of Xiao on...