2021 Workshop on Algebraic Geometry in Gunsan




21.11.18 - 21.11.21                      Ritz Plaza Hotel in Gunsan

Title/Abstract Home > Title/Abstract


김선자 (청운대)

- Title: Projectively normal embeddings of curves 

- Abstract: We first observe relations between projectively normal embeddings of curves and quadric hypersurfaces in a projective space. Through the observation we discuss conditions for very ample line bundles on multiple covers to fail to give projectively normal embeddings. Such conditions enable us to see that under some constraints every special very ample line bundle on a multiple cover embeds the curve as a projectively normal curve.


문현석 (KIAS) 

- Title: Rational Waring decomposition of monomials and integration of polynomials over a simplex

- Abstract: In this talk we consider the Waring rank of monomials over the rational numbers. We give a new upper bound for it by establishing a way in which one can take a structured apolar set for any given monomial. This bound coincides with all the known cases for the real rank of monomials, and is sharper than any other known bounds for the real Waring rank. Since all of the constructions are still valid over the rational numbers, this provides a new result for the rational Waring rank of any monomial as well. We also apply the methods developed in the paper to the problem of finding an explicit rational Waring decomposition of any homogeneous polynomial over rational numbers, which is important in many applications, especially to the integration of a polynomial over a simplex. We will present examples and computational implementation for potential use.


신재호 (KIAS) 

- Title: What is a Matroid? 

- Abstract: Matroids are ubiquitous due to their innate linearity. In this talk, I will introduce the definition of matroids with cryptomorphic axiomatizations and work out some examples.


이광우 (연세대)

- Title: Beauville involutions of Hilbert schemes of K3 surfaces 

- Abstract: For Hilbert schemes of K3 surfaces with particular Picard lattice, we consider Beauville involutions. In this talk, we discuss the relations among them including the natural automorphism induced from K3 surface.


이상현 (KIAS)

- Title: Survey on degeneracy loci and its application to enumerative geometry. 

- Abstract: I will survey on the cycles that come from the degeneracy condition of vector bundle homomorphisms. I will introduce some examples to explain how we can apply it to enumerative geometry.


이용남 (KAIST, IBS-CCG)  

- Title: Bigness of the tangent bundle of a Fano threefold with Picard number 2 which has a conic bundle structure 

- Abstract: Let $X$ be a Fano threefold with Picard number 2 which has a standard conic bundle structure over the projective plane. The degree of the discriminant curve in the projective pane can be from 2 to 6, or 8. In this talk, we will treat bigness property of the tangent bundle $T_X$ of $X$ by using total dual VMRT. This is an ongoing work, and a joint work with Hosung Kim and Jeong-Seop Kim. 


이철규 (KIAS) 

- Title: Do minimal weights determine a Hilbert point? 

- Abstract: There are many ways to classify projective schemes using minimal weights in the literature, such as analysis of GIT or K-stability. It is very natural to ask if minimal weights determine a Hilbert point. In this talk, we will rigorously state the problem and see many examples.


조용화 (KIAS)

- Title: Nodal-Severi varieties 

- Abstract: A nodal-Severi variety is the variety of nodal surfaces in $mathbb{P}^3$ having a fixed degree and a fixed number of nodes. We discuss a method to study nodal-Severi varieties via (half-)even sets of nodes which was first introduced by Beauville to study the maximal number of nodes in nodal quintic surfaces. More specifically, we discuss nodal-Severi varieties of degrees 5 and 6, based on the joint works in progress with Fabrizio Catanese, Stephen Coughlan, Davide Frapporti, Michael Kiermaier, and Sascha Kurz.


최준호 (KIAS)

- Title: A hierarchy of higher secant varieties

- Abstract: The study of higher secant varieties is a classical theme in projective algebraic geometry. In this talk, we present a hierarchy of higher secant varieties, and specify induced extremal and subextremal objects, namely higher secant varieties of minimal degree and del Pezzo higher secant varieties. Moreover, we characterize them in terms of the minimal free resolution (in other words, syzygies), and establish a connection with a conjecture called the generalized Bronowski's conjecture. This is a joint work with Prof. Sijong Kwak.