복소기하학연구단
Speaker Sandor Kovacs Univ. of Washington This is a report on joint work with Behrouz Taji. Given a flat projective morphism f : X → B of complex varieties, assuming that B is smooth, we construct a functorial system of reflexive Hodge sheaves on B . If in addition, X is also smooth then …
Speaker Young-Hoon Kiem Seoul National University The moduli space of n points on a projective line up to projective equivalence has been a topic of research since the 19th century. A natural moduli theoretic compactification was constructed by Deligne and Mumford as an algebraic stack. Later, Knudsen, Keel, Kapranov and others provided explicit …
Speaker Chenyang Xu Princeton Univ. K-stability of Fano varieties was initiated as a central topic in complex geometry, for its relation with the Kähler-Einstein metric. It turns out that the machinery of higher dimensional geometry, developed around the minimal model program, provides a fundamental tool to study it, and therefore makes it an …
Speaker Gunhee Cho UCSB We seek to gain progress on the following long-standing conjectures in hyperbolic complex geometry: prove that a simply connected complete Kähler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carathéodory-Reiffen metric does not vanish everywhere. As the next development of the important recent …
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 …