복소기하학연구단
List of Seminars A Hyperelliptic Curve Mapping to Specified Elliptic Curves Bo-Hae Im (KAIST) 14:00-15:00, IBS B266 Jordan Constants of Simple Abelian Varieties over Fields of Positive Characteristic WonTae Hwang (Jeonbuk National Univ.) 15:15-16:15, IBS B266 Decidable Diophantine Problems on Character Varieties Junho Peter Whang (Seoul National Univ.) 16:30-17:30, IBS B266
Speaker Bo-Hae Im KAIST (This is a part of Arithemetic Geometry Day in IBS-CCG.) We are interested in the existence and non-existence of rational curves on certain Kummer varieties which can be applied to the rank problem of quadratic twists of elliptic curves. In this talk, we prove that if the j-invariants of …
Speaker WonTae Hwang Jeonbuk National Univ. (This is a part of Arithemetic Geometry Day in IBS-CCG.) We compute the Jordan constants of simple abelian surfaces over fields of positive characteristic, with the aid of a similar computation on the Jordan constants of some arithmetic objects. As an update, we also briefly record a …
Speaker Junho Peter Whang Seoul National Univ. (This is a part of Arithemetic Geometry Day in IBS-CCG.) Character varieties of manifolds are basic objects in geometry and low-dimensional topology. We motivate the Diophantine study of their integral points. After discussing an effective finite generation theorem for integral points on SL2-character varieties of surfaces, …
Speaker Kang-Hyurk Lee GNU The Wong-Rosay theorem says that a smoothly bounded domain covering a compact complex manifold is biholomorphically equivalent to the unit ball. The general methodology of this theorem is the affine rescaling method. In this talk, I will introduce the potential rescaling method, an alternative of the affine rescaling. This …
Speaker Jeong-Seop Kim KAIST As well as the Hartshorne-Frankel conjecture on the ampleness of tangent bundle, it has been asked to characterize a smooth projective variety X whose tangent bundle TX attains certain positivity, e.g., nefness, k-ampleness, or bigness. But for the ampleness, the complete answers are not known even within the class …
Speaker Duc-Viet Vu Cologne I present a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, the result already gives a new Moser-Trudinger inequality for functions in the Sobolev space W1,2 of a domain in R2. As an application, we deduce a new necessary condition for …
Speaker Luca Rizzi IBS CCG Let f be a semistable fibration between a smooth complex variety of dimension n and a smooth complex curve. By a famous result of Fujita the direct image of the relative dualizing sheaf is the direct sum of a unitary flat vector bundle and an ample vector bundle. …
Speaker Guolei Zhong IBS CCG A Q-Cartier divisor on a normal projective variety is said to be strictly nef, if it has positive intersection with every integral curve. It has been a long history for people to measure how far a strictly nef divisor is from being ample. In this talk, I will …
Speaker Atsushi Ito Okayama Univ. Projective normality is an important property of ample line bundles on algebraic varieties. In this talk, I will explain that a general g-dimensional polarized abelian variety is projectively normal if χ(X, L) > 22g-1. We note that this bound is sharp. A key tool is basepoint-freeness threshold, which …
Speaker Yonghwa Cho IBS CCG It is a classical question to ask how many nodes may a surface contain. For sextics, the maximum number of nodes is 65, and is attained by Barth's example. We ask further: are all sextics with 65 nodes like Barth's example? To find an answer, we study even …
Speaker Hoseob Seo IBS CCG In L2 extension theorems from an irreducible singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure, which determines when a given function can be extended. In this talk, we show that the singularity of the Ohsawa measure can be …