A canonical Hodge theoretic projective structure on compact Riemann surfaces

Abstract: In this talk we will show the existence of a canonical projective structure on every compact Riemann surface, coming from Hodge theory. We will show that it differs from the canonical projective structure produced by the uniformisation theorem. In fact the (0,1)- component of the differential of the corresponding sections of the moduli space of projective structures over the moduli space of curves are different. The one corresponding to the projective structure coming from uniformisation was computed by Zograf and Takhtadzhyan as the Weil-Petersson Kaehler form on the moduli space of curves. Ours is the pullback via the Torelli map of a nonzero constant scalar multiple of the Siegel form on the moduli space of principally polarised abelian varieties. These are results obtained in collaboration with I. Biswas, E. Colombo and G.P. Pirola.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

If you use a calendar system, you can see the individual seminars at bit.ly/zag-seminar-calendar

Times vary to accommodate speakers time zones but times will be announced in GMT time.