Atsushi Ito, Projective Normality of General Polarized Abelian Varieties


     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

Dongsoo Shin, Deformations of Sandwiched Surface Singularities and the Semistable Minimal Model Program

B266 IBS

     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

Nam-Hoon Lee, Mirror Pairs of Calabi-Yau Threefolds from Mirror Pairs of Quasi-Fano Threefolds

B266 IBS

     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

Radu Laza, Deformations of Singular Fano and Calabi-Yau Varieties


     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

Keiji Oguiso, On Kawaguchi-Silverman Conjecture for Birational Automorphisms of Irregular Threefolds


     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

Brendan Hassett, Recent Progress and Questions on Stable Rationality


     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

Sheng Meng, Equivariant Kähler Model for Fujiki’s Class

B266 IBS

     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

Sung Rak Choi, On the Thresholds of Potential Pairs

B266 IBS

     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

Luca Rizzi, Local Systems, Algebraic Foliations and Fibrations


     Speaker Luca Rizzi IBS-CCG Given a semistable fibration f : X → B I will show a correspondence between foliations on X and local systems on B. Building up on this correspondence we will find conditions that give maximal rationally connected fibrations in terms of data on the foliation. We will develop the

Ziquan Zhuang, Boundedness of Singularities and Minimal Log Discrepancies of Kollár Components


     Speaker Ziquan Zhuang Johns Hopkins U Several years ago, Chi Li introduced the local volume of a klt singularity in his work on K-stability. The local-global analogy between klt singularities and Fano varieties, together with recent study in K-stability lead to the conjecture that klt singularities whose local volumes are bounded away from

Jakub Witaszek, Quasi-F-splittings


     Speaker Jakub Witaszek Princeton U What allowed for many developments in algebraic geometry and commutative algebra was a discovery of the notion of a Frobenius splitting, which, briefly speaking, detects how pathological positive characteristic Fano and Calabi-Yau varieties can be. Recently, Yobuko introduced a more general concept, a quasi-F-splitting, which captures much more

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