Fano manifolds from smoothing toroidal crossing varieties

Abstract: I am reporting on a joint work with Corti, Felten, Petracci where we put particular singular log structures on toroidal crossing spaces. We prove various properties of the resulting reflexive log differential forms from using local log smooth log crepant resolutions. The properties give the ingredients to conclude the Hodge to de Rham degeneration and the smoothability of the toroidal crossing Fano variety. All Fanos with very amply anticanonical divisor are obtained from so called "admissible" log singularties by this method. We believe that yet more general log singularities give all Fano manifolds with non-empty anticanonical class by similar methods.

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.