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fables [2023/04/20 21:28] – kalinin0fables [2023/12/05 11:54] (Version actuelle) – slavitya_gmail.com
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-  FABLES GEOMETRIQUES MINICOURSE, April 24-27Ìý+ Friday, Dec 8, 14h30, Salle 06-13Ìý
-  Sergey Finashin (METU Ankara)+Ìý
 +**Francesca Carocci (Genève)**Ìý
 +Ìý
 +**Degenerations of Limit linear series**Ìý
 +Ìý
 +Maps to projective space are given by basepoint-free linear series, thus these are key to understanding the extrinsic geometry of algebraic curves. Ìý
 +How does a linear series degenerate when the underlying curve degenerates and becomes nodal?Ìý
 +Eisenbud and Harris gave a satisfactory answer to this question when the nodal curve is of compact type. Eisenbud-Harris's theory of limit linear series gives proofs via degenerations  of many foundational results in Brill--Noether theory, and it is powerful enough to answer several  birational geometry questions on the moduli space of curves.Ìý
 +I will report on a joint work in progress with Lucaq Battistella and Jonathan Wise, in which we review this question from a moduli-theoretic and logarithmic perspective. The logarithmic prospective helps understanding the rich polyhedral and combinatorial structures underlying degenerations of linear series. These are linked with matroids and Bruhat-Titts buildings.Ìý
 +Ìý
 +----Ìý
 +Ìý
 +  Monday, Nov 13, 15h, Salle 06-13Ìý
 +  Ìý
 +**Francesca Carocci (Genève)**Ìý
 +  Ìý
 +**What can we do with the Logarithmic Hilbert Scheme?**  Ìý
 +  Ìý
 +In 2020 Maulik-Ranganathan defined the Logarithmic Hilbert-Scheme, which is interesting for the enumerative geometry of 3-folds;  for example, it gives access to degeneration techniques in sheaf-theoretic approaches to curve counting.  If we go one step back and look at degree d curves in toric surfaces,  the construction of the log Hilbert scheme has as a main ingredient the secondary fan of a toric fan, though as  moduli space of tropical plane curves up to translation.Ìý
 +Ìý
 +I will try to explain some of the ideas of the construction, trying to put emphasis on the tropical aspects of the theory.Ìý
 +Ìý
 +The main goal of the talk would be to understand if this theory gives rise to some interesting questions and the relation of such questions with tropical geometry.Ìý
 +Ìý
 +----Ìý
 +  May 22, salle 6-13, 15hÌý
 +Ìý
 +**Oleg Viro (Stony Brook)**Ìý
 +Ìý
 +**Simplest numerical invariants for some kinds of curves**Ìý
 +Ìý
 +In the 90s, Arnold introduced several numerical characteristics ofÌý
 +generic plane curves via axiomatic approach based on behavior of curvesÌý
 +under "perestroikas". Soon explicit formulas for the invariants haveÌý
 +been invented. The formulas have disclosed unexpected aspects of natureÌý
 +of the invariants and suggested various new objects to study, like realÌý
 +algebraic curves or circles inscribed in a generic plane curve.Ìý
 +Ìý
 +----Ìý
 +**FABLES GEOMETRIQUES MINICOURSE, April 24-27**Ìý
 +Ìý
   Lecture 1, Monday, April 24, 15h, room 6-13   Lecture 1, Monday, April 24, 15h, room 6-13
   Lecture 2, Tuesday, April 25, 13h, Room 1-07   Lecture 2, Tuesday, April 25, 13h, Room 1-07
   Lecture 3, Thursday, April 27, 16h15, Room 1-15   Lecture 3, Thursday, April 27, 16h15, Room 1-15
  
 +**Sergey Finashin (METU Ankara)**
  
 **Strong Invariants in Real Enumerative Geometry** **Strong Invariants in Real Enumerative Geometry**
fables.1682018935.txt.gz · Dernière modificationÌý: de kalinin0
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