﻿ 2021 Symposium in Algebraic Geometry 대수기하심포지엄
 2021 Symposium in Algebraic Geometry 대수기하 심포지엄 ( in memory of professor Bumsig Kim )     December 20, 2021                                    Online
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동수 (충남대학교)     Lecture Note ↓

- Title: All about deformations of cyclic quotient surface singularities

- Abstract: There are at least three different ways of describing deformations of cyclic quotient surface singularities: Equations, picture deformations, P-resolutions. We analyze the correspondence between them by the semi-stable minimal model program for 3-folds. This is an application of the joint work with Heesang Park on deformations of sandwiched surface singularities.

최준호 (고등과학원)     Lecture Note

- Title: Higher secant varieties and the identifiability

- Abstract: The identifiability is a notion on higher secant varieties, and a tangential projection criterion for it is suggested by the generalized Bronowski’s conjecture. In this talk, we introduce our results on the conjecture; one amounts to algebraic part of the conjecture, and another gives a syzygetic characterization of higher secant varieties of minimal degree. This is a joint work with Prof. Sijong Kwak.

홍규식 (전주대학교)     Lecture Note ↓

- Title: Hypersurfaces with defect

- Abstract: A projective hypersurface X⊆P^n has defect if h^i(X)≠h^i(Pn) for some i∈{n,…,2n−2} in a suitable cohomology theory. A hypersurface with defect is necessarily singular. It seems that defect forces the hypersurface to have many singularities compared to their degree.
Q1) Zero defect
This occurs for example when X⊆P^4 is factorial. In this talk, we present some factorial 3-folds.
Q2) Positive defect
For example, am important class of hypersurfaces with positive defect is formed by non-factorial hypersurfaces in P^4. By a result of Niels Linder, in characteristic 0, the Tjurina number of hypersurfaces with positive defect is large. Also, for X with mild singularities, there is a similar result in positive characteristic. As an application, he obtain a lower bound on the asymptotic density of hypersurfaces without defect over a finite field. We plan to generalize this result to the Grassmannian Gr(2,4).

황원태 (전북대학교)     Lecture Note ↓

- Title : Jordan constants of the automorphism group of simple abelian surfaces over fields of positive characteristic

- Abstract : In this talk, we rather completely describe the Jordan constants of the multiplicative subgroups of quaternion algebras over some number fields of small degree, and then apply the description to obtain a new result on the computation of the precise Jordan constants of the multiplicative subgroup of the endomorphism algebras (, whence the automorphism group) of simple abelian surfaces over fields of positive characteristic. We also briefly summarize what were known in this direction in char 0.
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