복소기하학연구단
Speaker Olivier Martin Stony Brook Univ. I will discuss recent work in collaboration with R. Lazarsfeld which explores the following question: Given varieties X and Y of the same dimension how far are they from being birational? I will define various "measures of association" which quantify the failure of X and Y to …
Speaker Kento Fujita Osaka Univ. There are 105 irreducible families of smooth Fano threefolds, which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kähler-Einstein metric or not. This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus …
Speaker Sanghoon Baek KAIST Consider the canonical morphism from the Chow ring of a smooth variety X to the associated graded ring of the coniveau filtration on the Grothendieck ring of X. In general, this morphism is not injective. However, Nikita Karpenko conjectured that these two rings are isomorphic for a generic flag …
Speaker Rostislav Devyatov KAIST In the first part of my talk I am going to speak about Schubert calculus. Let G/B be a flag variety, where G is a linear simple algebraic group, and B is a Borel subgroup. Schubert calculus studies (in classical terms) multiplication in the cohomology ring of a flag …
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 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 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 …