복소기하학연구단
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 …
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 Slawomir Dinew Jagiellonian University, Krakow Extension problems through a small singular set appear throughout complex analysis. After a short reminder of some classical results we shall focus on problems of extending (pluri)subharmonic functions. In particular we shall focus on new techniques coming from PDEs that lead to resolutions of several questions in …
Speaker Tsz On Mario Chan Pusan National University In this talk, we introduce a modification of the analytic adjoint ideal sheaves. The original analytic adjoint ideal sheaves were studied by Guenancia and Dano Kim. The modified version makes use of the residue functions with respect to log-canonical (lc) measures, giving a sequence of …
Speaker Ngoc-Son Duong University of Vienna In this talk, we will discuss a complete classification of proper holomorphic maps from the unit ball in complex two dimensional space into the Cartan's classical domain of type IV in complex three dimensional space that extend smoothly to some boundary point. This classification (which is a …
Speaker Hoang-Chinh Lu Université Paris-Saclay, Orsay We investigate in depth the behaviour of Monge-Ampère volumes of quasi-psh functions on a given compact hermitian manifold. We prove that the property for these Monge-Ampère volumes to stay bounded away from zero or infinity is a bimeromorphic invariant. We show in particular that a conjecture of …
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 …