Arithemetic Geometry Day in IBS-CCG

B266 IBS, Korea, Republic of

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

Bo-Hae Im, A Hyperelliptic Curve Mapping to Specified Elliptic Curves

B266 IBS, Korea, Republic of

     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

WonTae Hwang, Jordan Constants of Simple Abelian Varieties over Fields of Positive Characteristic

B266 IBS, Korea, Republic 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

Junho Peter Whang, Decidable Diophantine Problems on Character Varieties

B266 IBS, Korea, Republic of

     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,

Kang-Hyurk Lee, Smoothly Bounded Domain with a Compact Quotient

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     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

Jeong-Seop Kim, Positivity of Tangent Bundles of Fano Threefolds

TBA

     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

Duc-Viet Vu, Moser-Trudinger Inequalities and Complex Monge-Ampere Equations

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     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

Guolei Zhong, Strictly Nef Divisors on Singular Varieties

TBA

     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

Atsushi Ito, Projective Normality of General Polarized Abelian Varieties

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     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

Yonghwa Cho, Nodal Sextics and Even Sets of Nodes

B234

     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

Hoseob Seo, On L2 Extension from Singular Hypersurfaces

B234

     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

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