Jump to content

File:Barbara Fantechi on Algebraic Geometry at Stanford.jpg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (602 × 789 pixels, file size: 71 KB, MIME type: image/jpeg)

Summary

Description
English: Barbara Fantechi (Oct. 16, 2020): Infinitesimal deformations of semi-smooth varieties

This is a report on joint work with Marco Franciosi and Rita Pardini. Generalizing the standard definition for surfaces, we call a variety X (over an algebraically closed field of characteristic not 2) {\em semi-smooth} if its singularities are \'etale locally either uv=0 or u^2=v^2w (pinch point); equivalently, if X can be obtained by gluing a smooth variety (the normalization of X) along an involution (with smooth quotient) on a smooth divisor. They are the simplest singularities for non normal, KSBA-stable surfaces. For a semi-smooth variety X, we calculate the tangent sheaf T_X and the infinitesimal deformations sheaf {\mathcal T}^1_X:={\mathcal E}xt^1(\Omega_X,\mathcal O_X) which determine the infinitesimal deformations and smoothability of X.

As an application, we use Tziolas' formal smoothability criterion to show that every stable semi-smooth Godeaux surface (classified by Franciosi, Pardini and S\"onke) corresponds to a smooth point of the KSBA moduli space, in the closure of the open locus of smooth surfaces.
Date
Source Barbara Fantechi (Oct. 16, 2020): Infinitesimal deformations of semi-smooth varieties at 1:00:41, cropped, brightened
Author Algebraic Geometry at Stanford

Licensing

This video, screenshot or audio excerpt was originally uploaded on YouTube under a CC license.
Their website states: "YouTube allows users to mark their videos with a Creative Commons CC BY license."
To the uploader: You must provide a link (URL) to the original file and the authorship information if available.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
This file, which was originally posted to an external website, has not yet been reviewed by an administrator or reviewer to confirm that the above license is valid. See Category:License review needed for further instructions.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

20 April 2021

image/jpeg

7dbb48759206bd0c4883dbc9866a0efdb8c0d6c7

72,888 byte

789 pixel

602 pixel

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:02, 13 September 2022Thumbnail for version as of 15:02, 13 September 2022602 × 789 (71 KB)GRuban{{Information |description={{en|1=Barbara Fantechi (Oct. 16, 2020): Infinitesimal deformations of semi-smooth varieties This is a report on joint work with Marco Franciosi and Rita Pardini. Generalizing the standard definition for surfaces, we call a variety X (over an algebraically closed field of characteristic not 2) {\em semi-smooth} if its singularities are \'etale locally either uv=0 or u^2=v^2w (pinch point); equivalently, if X can be obtained by gluing a smooth variety (the normaliza...

Global file usage

The following other wikis use this file: