SISSA Algebraic geometry seminars in presence and online

[Michele Graffeo]

LAST seminar, Friday 22/06/2022 at 4:30pm, room to be announced (NOTICE THE UNUSUAL SCHEDULE)

Speaker: Barbara Fantechi (SISSA)

Title: Smoothability of non normal stable Gorenstein Godeaux surfaces

Abstract: This is joint work with Marco Franciosi and Rita Pardini.
Godeaux surfaces, with K^2=1 and p_g=q=0, are the (complex projective) surfaces of general type with the smallest possible invariants. A complete classification, i.e. an understanding of their moduli space, has been an open problem for many decades.

The KSBA (after Kollár, Sheperd-Barron and Alexeev) compactification of the moduli includes so called stable surfaces. Franciosi, Pardini and Rollenske classified all such surfaces in the boundary (i.e., not normal) which are Gorenstein (i.e., not too singular).

The simplest possible singularities are semi-smooth, ie a double curve with finitely many pinch points.

We prove that stable Godeaux semi-smooth surfaces corresponds to a point in the moduli which is nonsingular of the expected dimension 8. We expect that the methods used (which include classical and recent infinitesimal deformation theory, as well as algebraic stacks and the cotangent complex) can be applied to other cases, and to more general moduli as well.


You can find more information about the seminars of the algebraic geometry group at the following links.
https://graffeomichele.github.io/seminari.html
https://www.math.sissa.it/content/algebraic-geometry-seminar-20212022

Join Zoom Meeting
https://sissa-it.zoom.us/j/83917587333?pwd=amVZSW54bkROS2U0Ly9HbVJYK3c2QT09

Meeting ID: 839 1758 7333
Passcode: 712636