TITLE and ABSTRACT
○ Jaehyouk Lee 이재혁 교수 (Ehwa Womans University, 이화여대)
○ Jaehyouk Lee 이재혁 교수 (Ehwa Womans University, 이화여대)
TITLE: Special divisors of del Pezzo surfaces and ADE polytopes
TITLE: Special divisors of del Pezzo surfaces and ADE polytopes
The geometry of del Pezzo surface is full of wonderful and mysterious symmetries. Especially, we consider the correspondence between special divisor classes so called the lines of del Pezzo surface and the vertices of Gosset polytopes. Therefrom we can explain various mysterious symmetries. In this talk, we introduce special divisor classes according to the geometry of Gosset polytopes and explain the correspondences between these divisors and subpolytopes. Moreover, we apply the correspondence to study the configuration of lines of del Pezzo surfaces.
The geometry of del Pezzo surface is full of wonderful and mysterious symmetries. Especially, we consider the correspondence between special divisor classes so called the lines of del Pezzo surface and the vertices of Gosset polytopes. Therefrom we can explain various mysterious symmetries. In this talk, we introduce special divisor classes according to the geometry of Gosset polytopes and explain the correspondences between these divisors and subpolytopes. Moreover, we apply the correspondence to study the configuration of lines of del Pezzo surfaces.
○ Shinnosuke Okawa 大川 新之介 교수 (Osaka University, 오사카대학교)
○ Shinnosuke Okawa 大川 新之介 교수 (Osaka University, 오사카대학교)
TITLE: Derived equivalence and Grothendieck ring of varieties
TITLE: Derived equivalence and Grothendieck ring of varieties
Smooth projective varieties are said to be D-equivalent if the bounded derived categories of coherent sheaves are equivalent as triangulated categories. Though D-equivalent varieties are not necessarily birational, it is expected that some of the basic invariants should coincide.
Smooth projective varieties are said to be D-equivalent if the bounded derived categories of coherent sheaves are equivalent as triangulated categories. Though D-equivalent varieties are not necessarily birational, it is expected that some of the basic invariants should coincide.
Recently a couple of interesting examples of Calabi-Yau manifolds have been discovered and, inspired by these examples, the following question was asked; does D-equivalence imply L-equivalence? Here, two varieties are said to be L-equivalent if they have the same class in the localization of the Grothendieck ring of varieties by the class of the affine line.
Recently a couple of interesting examples of Calabi-Yau manifolds have been discovered and, inspired by these examples, the following question was asked; does D-equivalence imply L-equivalence? Here, two varieties are said to be L-equivalent if they have the same class in the localization of the Grothendieck ring of varieties by the class of the affine line.
In this talk I would briefly review this topic and discuss the case of abelian varieties. It turns out that the original question has to be fixed. I will also give possible modification(s) of the question
In this talk I would briefly review this topic and discuss the case of abelian varieties. It turns out that the original question has to be fixed. I will also give possible modification(s) of the question
○ Taro Sano 佐野 太郎 교수 (Kobe University, 고베대학교)
○ Taro Sano 佐野 太郎 교수 (Kobe University, 고베대학교)
Title: Effective non-vanishing for weighted complete intersections
Title: Effective non-vanishing for weighted complete intersections
Adjoint and nef line bundles of the form K_X + L play an important role in higher dimensional algebraic geometry. A conjecture of Ambro and Kawamata says that this has a non-zero section. This conjecture is widely open. As a test case, I'll show that this is true for Fano or Calabi-Yau quasi-smooth weighted complete intersections. I'll also briefly explain some general preliminaries on weighted complete intersections
Adjoint and nef line bundles of the form K_X + L play an important role in higher dimensional algebraic geometry. A conjecture of Ambro and Kawamata says that this has a non-zero section. This conjecture is widely open. As a test case, I'll show that this is true for Fano or Calabi-Yau quasi-smooth weighted complete intersections. I'll also briefly explain some general preliminaries on weighted complete intersections
○ Insong Choe 최인송 교수 (Konkuk University, 건국대학교)
○ Insong Choe 최인송 교수 (Konkuk University, 건국대학교)
TITLE: Lagrangian Quot schemes over an algebraic curve
TITLE: Lagrangian Quot schemes over an algebraic curve
In this talk, I would like to report on our results on the ongoing project with Daewoong Cheong and George H. Hitching. The aim of the project is to compute the number of maximal Lagrangian subbundles of a general symplectic bundle over a curve.
In this talk, I would like to report on our results on the ongoing project with Daewoong Cheong and George H. Hitching. The aim of the project is to compute the number of maximal Lagrangian subbundles of a general symplectic bundle over a curve.
To apply the Vafa-Intriligator formula, we need to define another intersection number on Lagrangian quot schems and justify that two numbers are equal. In this perspective, we study the basic properties of the Lagrangian quot schemes over an algebraic curve
To apply the Vafa-Intriligator formula, we need to define another intersection number on Lagrangian quot schems and justify that two numbers are equal. In this perspective, we study the basic properties of the Lagrangian quot schemes over an algebraic curve
○ Dano Kim 김다노 교수(Seoul National University, 서울대학교)
○ Dano Kim 김다노 교수(Seoul National University, 서울대학교)
TITLE: L2 extension and subadjunction
TITLE: L2 extension and subadjunction
L2 extension theorems of Ohsawa-Takegoshi type from complex analysis are analogous to Kodaira type vanishing theorems but with added crucial strength given by L2 estimates and much weaker curvature conditions. They are expected to play an important role in the full minimal model program. For that purpose, our previous work enlarged the range of applicability of L2 extension by considering the setting of a log canonical center and made connection with Kawamata's subadjunction. Recently this setting was revisited by Demailly where fiber integral along a submersion was used among other things. In this talk, we will discuss the relation of these works and new results obtained from combining these approaches.
L2 extension theorems of Ohsawa-Takegoshi type from complex analysis are analogous to Kodaira type vanishing theorems but with added crucial strength given by L2 estimates and much weaker curvature conditions. They are expected to play an important role in the full minimal model program. For that purpose, our previous work enlarged the range of applicability of L2 extension by considering the setting of a log canonical center and made connection with Kawamata's subadjunction. Recently this setting was revisited by Demailly where fiber integral along a submersion was used among other things. In this talk, we will discuss the relation of these works and new results obtained from combining these approaches.