Algebraic geometry seminars in presence and online

[Alessandro Nobile]

Next seminar is scheduled for Friday 1/04/2022 at 4:30pm, room Boris Dubrovin 136 or Zoom (see below).

Speaker: Michele Graffeo (Sissa)

Title:  On the Behrend function and the blowup of some fat points

Abstract: Not much is known about the geometric properties of the punctual Hilbert scheme of fat points of length n supported at the origin of the affine plane A^2. In order to investigate them, a huge number of invariants, for fat points, has been introduced (e.g. multiplicity, order, type, blowup tree...). I will focus on the Behrend number v_Z of a fat point Z in A^2. Such invariant can be defined in terms of the blowup of the affine plane with center the subscheme  Z. I will discuss the problem of computing the Behrend number of a monomial fat point following a joint work with Andrea T. Ricolfi. In particular, I will explain, first in the normal setting, how toric geometry methods apply in the construction of the blowup and in the computation of v_Z. Then, I will move to the non-normal setting, and I will show some examples of computation. Finally, if time permits, I will show some difficulties that arise in higher dimension.



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


Meeting ID: 839 1758 7333
Passcode: 712636