Conference - Affine Geometry and Birational Geometry
Feb 9-13, 2025
SKYBAY Hotel Gyeongpo

Abstracts (Download PDF)

• Atsushi Ito (University of Tsukuba)
  Title: On estimation of Seshadri constants
  Abstract: Seshadri constant is an invariant which measures the positivity of ample line bundles on projective varieties. In general, it is difficult to compute or estimate this invariant. In this lecture, I will explain some basic properties of Seshadri constant and how to estimate it.
  
  

• Masatomo Sawahara (Hirosaki University)
  Title: Polarized cylinders in Du Val del Pezzo surfaces
  Abstract: Polarized cylinders in normal projective varieties receive much attention from the viewpoint of connecting unipotent group actions on affine algebraic varieties. Hence, we shall focus on configuring cylindrical ample sets of normal projective varieties. In a previous work, Cheltsov, Park and Won studied cylindrical ample sets of smooth del Pezzo surfaces. In this talk, we will discuss the configuration of cylindrical ample sets of Du Val del Pezzo surfaces of degree at least 2.

• Takashi Kishimoto (Saitama University)
  Title: Forms of cylindrical Fano threefolds
  Abstract: The cylindricity of Fano varieties is to some extent related to the K-stability and unipotent geometry, e.g., a recent work due to Kim-Kim-Won. In order to find cylinders in Fano varieties, it is sometimes essential to seek those contained in Mori fiber spaces, where cylinders compatible with a structure of Mori fiber spaces arise from those contained in the corresponding generic fibers and vice versa. From this viewpoint, the cylinders on rank one Fano varieties defined over a field of characteristic zero, which is not necessarily algebraically closed, play an important role. In the talk, we focus on the cylindricity of forms of rank one smooth Fano threefolds, especially forms of the projective 3-space, the smooth quadric hypersurface, the smooth quintic del Pezzo threefold and prime Fano threefolds of degree 22. This is based on the joint work in progress with Adrien Dubouloz and Kento Fujita.

• Kiryong Chung (Kyungpook National University)
  Title: Rational curves in the Mukai-Umemura variety
  Abstract:  Let X be the prime Fano threefold of index one, degree 22, and Pic(X)=Z. Such a threefold X can be realized by a regular zero section s of \bigwedge^2 (F^{*\oplus 3}) over a Grassmannian variety Gr(3,V), dim V=7 with the universal subbundle F. If the section s is given by the net of the SL_2-invariant skew forms, we call it by Mukai-Umemura (MU) variety. In this talk, we prove that the Hilbert scheme of rational quartic curves in the MU-variety is smooth and compute its Poincare polynomial by applying the Bia{\l}ynicki-Birula's theorem. If time is allowed, we discuss global picture of the moduli space of rational quartic curves through the Sarkisov link. This is a joint work with Jaehyun Kim (EWU) and Jeong-Seop Kim (KIAS).

• Dae-Won Lee (Ewha Womans University)
  Title: On the existence of anticanonical minimal model
  Abstract: Recently, there have been remarkable developments in the minimal model program. The minimal model program is a sequence of birational contractions which makes a canonical divisor to a nef divisor. In this talk, we report some recent progress on the existence of the anticanonical minimal model.

• Kwangwoo Lee (KIAS)
  Title: Automorphisms of the Hilbert square of Cayley's K3 surface
  Abstract: We will show that the automorphism group of the Hilbert square of Cayley's K3 surface is a free product of three cyclic groups of order two. For this result, we use the characteristics of natural automorphisms on Hilbert squares and the geometry of the hyperbolic plane.