Geometry of secants
October 24th-28th, 2022
IMPAN, Warsaw, Poland
The workshop "Geometry of Secants" is dedicated to classical algebraic geometry related to secant varieties and decompositions. We plan to cover topics that are close to Terracini- and Scorza-style geometry, also with relations to birational problems, and other stuff about secant varieties, mainly focusing on aspects of interest for algebraic geometers.
List of topics:
- defectivity of secant varieites,
- singularities of secant varieties,
- defining ideals of secant varieties,
- configurations of points on projective manifolds,
- linear systems on projective varieties and manifolds that are related to secant varieties,
- elementary scheme-theoretic methods,
- dual varieties.
During the group discussions, participants raised interest on some open questions. The list of these conjectures and problems is here.
- Hirotachi Abo (University of Idaho, Moscow, ID, USA),
- Alex Casarotti (University of Trento, Italy),
- Junho Choe (Korea Institiute of Advanced Study, Seoul, Korea),
- Ciro Ciliberto (University of Rome Tor Vergata, Italy),
- Sandra Di Rocco (KTH Royal Institute of Technology, Stockholm, Sweden),
- Alessandro Gimigliano (University of Bologna, Italy),
- Kangjin Han (Daegu-Gyeongbuk Institute of Science & Technology, Korea),
- Michał Kapustka (Institute of Mathematics of Polish Academy of Sciences, Poland),
- Antonio Laface (University of Concepción, Chile),
- Alex Massarenti (University of Ferrara, Italy),
- Giorgio Ottaviani (University of Florence, Italy),
- Elisa Postinghel (University of Trento, Italy),
- Kristian Ranestad (University of Oslo, Norway),
- Douglas Torrance (Piedmont University, Demorest, GA, USA),
- Nick Vannieuwenhoven (Catholic University of Leuven, Belgium).
The workshop takes place at Institute of Mathematics of Polish Academy of Sciences (IMPAN). The address is Śniadeckich 8, 00-656 Warsaw, Poland. Lectures will take place in room number 321 on the third floor.
Some hints on the accommodation are available at the AGATES accommodation tab. Note that some supported participants must reserve their accommodations through the University of Warsaw, see the above webpage for details.
As of now, we plan the workshop as an in-person event and we do not foresee any possibility of on-line participation.
Monday, Oct 24
|Tuesday, Oct 25||Wednesday, Oct 26||Thursday, Oct 27||
Friday, Oct 28
|| Han [slides]
|| Choe [slides]
|| Coffee break, room 409
||Coffee break, room 409||Coffee break, room 409||Coffee break, room 409||Coffee break, room 409|
||Di Rocco||Ranestad||Ottaviani|| Ciliberto [slides]
|Gimigliano [slides]|| Laface [slides]
|| Torrance [slides]
||Lunch break|| Lunch break
||(free afternoon)||Lunch break||Lunch break|
|| Discussions and working groups, phrasing the problems, initial questions, room 321
|| Discussions and working groups, rooms 6, 321, 408
|Discussions and working group, rooms 6, 321, 408|| Discussions and working groups, general assembly, room 321
||Coffee break, room 409|| Coffee break, room 409
||(free afternoon)||Coffee break, room 409||Coffee break, room 409|
|| Discussions and working groups, dividing into problem groups
|| Discussions and working groups, general assembly, room 321
||(free afternoon)||Discussions and working group, rooms 6, 321, 408|
Prerequisites and preworkshop teach-in
Speakers of the workshop will freely use several concepts that are common to the topics addressed at the workshops: secant varieties, expected dimension, apolarity action, Hilbert function, various notions of rank, identifiability, Terracini's Lemma. For participants' convenience we prepared a brief cheat sheet ("ściąga" in Polish) with such definitions and their basic properties (the file will be updated soon). In addition, during the week prior to the workshop there was a special meeting (in hybrid format) when you can ask questions and comment on those notions. This teach-in meeting was on Thursday, 20 Oct at 16:10 (in hybrid format: at IMPAN room 405, and via zoom).
- Terracini Loci and high Veronese of X is non-defective, room 321.
- Secants of low degree, room 6.
- Subschemes of P^2, room 408.
To attend, please fill in the AGATES registration form, indicating that you plan to attend the workshop in the section "Interest in events".
Financial support and institutions involved
- IDUB thematic research program of University of Warsaw,
- Banach Center,
- National Science Center of Poland.
The workshop is a part of a semester long program Algebraic Geometry with Applications to TEnsors and Secants (AGATES), which is supported by the Simons Foundation and by Institute of Mathematics of Polish Academy of Sciences.