Apr. 29 (Friday) 09:00AM-10:00AM
Speaker: Jayan Mukherjee (Brown University)
Title: Deformations and moduli of irregular canonical covers with $K^2=4p_g-8$
Abstract: In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying $K^2 = 4p_g-8$, for any even integer $p_g \geq 4$. These surfaces also have unbounded irregularity $q$. We carry out our study by investigating the deformations of the canonical morphism $\varphi: X \to \mathbb{P}^N$, where $\varphi$ is a quadruple Galois cover of a smooth surface of minimal degree. As a result, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality $p_g > 2q-4$, with an irreducible component that has a proper “quadruple” sublocus where the degree of the canonical morphism jumps up. The existence of jumping subloci is a contrast with the moduli of surfaces with $K^2 = 2p_g- 4$, studied by Horikawa. These irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus $g\geq 3$, for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational.
Location: Rm. 515, NCTS (Cosmology Bldg., NTU)