복소기하학연구단
Speaker Yan Li Beijing Institute of Technology Let $G$ be a connected, reductive, linear algebraic group that acts on a normal variety $X$, and $B$ be a Borel subgroup group of $G$. The complexity of the $G$-action on $X$ was defined by E. B. Vinberg in 1985 as the codimension of $B$-orbit at …
Speaker Yan Li Beijing Institute of Technology Let $G$ be a connected, reductive, linear algebraic group that acts on a normal variety $X$, and $B$ be a Borel subgroup group of $G$. The complexity of the $G$-action on $X$ was defined by E. B. Vinberg in 1985 as the codimension of $B$-orbit at …
Speaker Daebeom Choi University of Pennsylvania In this talk, we discuss the existence and nonexistence of certain birational contractions of \(\overline{\mathrm{M}}_{g,n}\). Somewhat surprisingly, this depends on the characteristic of the base field: many such contractions exist only in positive characteristic. We present a precise form of this phenomenon and discuss two examples that …
Speaker Yunhyung Cho Sungkyunkwan University It is well known that there is a bijective correspondence between the set of positive integer solutions to the Markov equation and the set of Fano triangles mutation equivalent to the Fano triangle of $\mathbb{P}^2$. In this talk, we establish a higher dimensional generalization of this correspondence for …
Speaker Sung Gi Park Princeton University I will discuss the indeterminacy locus of the period map from the moduli space of hypersurfaces to the period domain and its compactifications. In the case of quartic K3 surfaces, the result verifies the expectation of Laza and O'Grady that the period map from the GIT compactification …
Speaker Hyunsuk Kim University of Michigan Considering the singular cohomology of a cubic fourfold yields a morphism from the moduli space of (smooth) cubic fourfolds to the period domain. Both spaces have natural compactifications, the GIT moduli space of cubic fourfolds parametrizing all GIT polystable objects, and the Baily-Borel compactification of the period …
Speakers Woohyeok Jo (Seoul National U.) Jongil Park (Seoul National U.) Kyungbae Park (Kangwon National U.) Abstracts PDF file Schedule August 7 (Fri) 10:30-12:00 Jongil Park 14:00-15:30 Woohyeok Jo August 8 (Sat) 10:30-12:00 Kyungbae Park 14:00-16:00 Jongil Park & Kyungbae Park Organizers JongHae Keum (KIAS) DongSeon Hwang (IBS-CCG) Venue 8101, KIAS, Seoul, Korea
Speaker Guolei Zhong East China Normal University Positivity properties of tangent sheaves are known to impose strong restrictions on the global geometry of projective varieties and, more generally, compact Kähler varieties. In this talk, after briefly reviewing the background, we will present several structural results for compact Kähler varieties with pseudo-effective tangent sheaf. …
Speaker David Sykes IBS-CCG This talk will introduce a natural construction for encoding codimension 1 pseudo-product structures into filtered manifolds amenable to analysis by Tanaka prolongation techniques, and its application to local geometry of CR hypersurfaces. Classically, Tanaka prolongation has only been applicable to maximally nondegenerate pseudo-product structures, while our new techniques require …
Speaker Sönke Rollenske Marburg University In the study of (relatively minimal) elliptic surfaces $f\colon S \to C$ with a section, the Weierstrass model plays an important role. We discuss two different models for elliptic surfaces with a bisection (or more generally an $f$-nef divisor which has degree two on the fibres): a birational …
Speaker Sönke Rollenske Marburg University Compact quotients of non-abelian complex nilpotent Lie groups are non-Kähler manifolds with trivial canonical bundle, the most prominent example being the Iwasawa manifold. We give a precise characterisation of the (rare) cases where deformations of such manifolds are unobstructed in terms of so-called verbal ideals in free nilpotent …
Speaker Yewon Luke Cho Gyeongsang National U A characterization of noncompact ball quotients by Munteanu (2009) implies that only complete Kähler-Einstein metrics on certain noncompact ball quotients maximize the bottom of the spectrum among complete Kähler metrics with Ricci curvature bounded below by -1. In this talk, I will report my recent observation, …