복소기하학연구단
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 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 Dongsoo Shin Chungnam National Univ. A sandwiched surface singularity is a rational surface singularity that admits a birational map to the complex projective plane. de Jong and van Straten prove that deformations of sandwiched surface singularities are induced from special deformations of germs of plane curve singularities (called picture deformations). On the …
Speaker Nam-Hoon Lee Hongik Univ. We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations using conjectures about Landau-Ginzburg models. Utilizing this notion, we give pairs of normal …
Speaker Radu Laza Stony Brook University It is well known that Calabi-Yau manifolds have good deformation theory, which is controlled by Hodge theory. By work of Friedman, Namikawa, M. Gross, Kawamata, Steenbrink and others, some of these results have been extended to Calabi-Yau threefolds with canonical singularities. In this talk, I will report …
Speaker Keiji Oguiso Univ. of Tokyo This is a joint work in progress with Professors Jungkai-Alfred Chen and Hsueh-Yung Lin. We study the main open parts of Kawaguchi-Silverman Conjecture (KSC), asserting that for a birational self-map f of a smooth projective variety X defined over K, the arithmetic degree αf(x) exists and coincides …
Speaker Brendan Hassett ICERM / Brown Univ. A complex variety X is rational if its field of meromorphic functions is isomorphic to C(t1, ..., td), the function field of projective space Pd. It is stably rational if X × Pm is rational for some m. Topological and complex invariants give criteria for whether …
Speaker Sheng Meng KIAS Let X be a compact complex manifold in Fujiki's class C, i.e., admitting a big (1,1)-class . Consider Aut(X) the group of biholomorphic automorphisms and Aut(X) the subgroup of automorphisms preserving the class via pullback. We show that X admits an Aut(X)-equivariant Kähler model: there is a bimeromorphic holomorphic …
Speaker Sung Rak Choi Yonsei Univ. Choi-Park first introduced and develped the notion of potential pairs. The notion was designed to control the singularities of the outcome of the 'anticanonical' minimal model program. In this talk, after reviewing the properties of potnetial klt pairs, we examine the ACC property of the potential lc …
Speaker Christian Schnell Stony Brook Univ. The theory of variations of Hodge structure has many applications in algebraic geometry. Most of these are based on the results by Schmid, Cattani, Kaplan, Kashiwara, and Kawai from the 1970s and 1980s. I will describe a new approach that proves these results — such as the …