Junyan Zhao (Illinois) скачать в хорошем качестве

Junyan Zhao (Illinois)

Junyan Zhao (Illinois) 13 July 2023 "Moduli of curves of genus 6 and K-stability" In this talk, I will describe a way to study moduli of curves of small genus (eg. g=3,4,6) via K-stability. For instance, a general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X_5 as a divisor of class -2K_{X_5}. Thus the K-moduli spaces of the pair (X_5, cC) are birational to the moduli of DM-stable curves \bar{M_6}. On the other hand, X_5 can be embedded in P^1 x P^2 as a divisor of class O(1,2), under which -2K_X is linearly equivalent to O_X(2,2). One can study the VGIT-moduli spaces in this setting. In this talk, I will compare these various compactifications of moduli spaces. Slides for this talk are available at: https://kasprzyk.work/seminars/pdf/Zh... Visit the Online Algebraic Geometry Seminar webpage at: https://kasprzyk.work/seminars/ag.html