복소기하학연구단
Speaker Sung Gi Park Princeton U. / IAS The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge-Du …
Alex Abreu Visitor (2025.6.25-2025.7.5) from Universidade Federal Fluminense
Speaker Yoosik Kim Pusan National University According to the Kempf–Ness theorem, the GIT quotient is equivalent to the symplectic reduction. Using this correspondence, we explain how to relate the counting of holomorphic disks between a symplectic manifold equipped with a Hamiltonian group action and its symplectic reduction. As an application, we derive the …
Speaker Alex Abreu Universidade Federal Fluminense The classical Torelli theorem states that a smooth curve can be recovered from its polarized Jacobian. In this talk, we will discuss the extensions of this theorem to stable curves and their dual graphs, as well as its dependence on the concept of compactified Jacobians. First, we …
This workshop brings together experts in Hessenberg varieties, Lusztig varieties, and the affine Grassmannian. It focuses on the rich interactions among these geometric objects and their connections to representation theory and combinatorics. Recent breakthroughs and new developments will be presented and discussed. The workshop aims to foster collaboration and inspire future research. Invited Speakers …
Speaker Yoonjoo Kim Columbia U. I would like to report two ongoing results on Lagrangian fibrations of smooth symplectic varieties. The first is the construction of a delta-regular smooth group scheme that acts on a given Lagrangian fibration. It is a generalization of the result of Arinkin-Fedorov, who proved the result under the …
Speaker Hyukmoon Choi IBS CCG and KAIST A projective variety V is an equivariant compactification of an algebraic group G if there exists an algebraic G-action on V with a Zariski open orbit O, which is equivariantly biregular to G. Such a G-action is called an equivariant compactification (EC) structure on V. For …
Speaker Makoto Enokizono University of Tokyo Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the equality of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces. …
Speaker Doyoung Choi KAIST / IBS We study the higher secant varieties of a smooth projective variety embedded in projective space. We prove that when the variety is a surface and the embedding line bundle is sufficiently positive, these varieties are normal with Du Bois singularities and the syzygies of their defining ideals …
Speaker Haesong Seo KAIST / IBS A projective manifold is called hyperbolic if it does not admit an entire map from the complex plane. Demailly proved that hyperbolic manifolds are algebraically hyperbolic, meaning that there are degree bounds for curves in terms of their genera. It is a highly challenging problem to determine …
Speaker Qifeng Li Shandong University Let X be a smooth equivariant compactification of a symmetric space. In this talk, we will discuss when a minimal rational curve on X is the orbit closure of a 1-parameter group. In case the symmetric space is of group type, the answer is positive and moreover the …
Speaker Yong Hu Shanghai Jiao Tong University In this talk, we will introduce the 3-dimensional Noether inequality and completely classify the canonical threefolds on the Noether line with $p_g \ge 5$ by studying their moduli spaces. For every such moduli space, we establish an explicit stratification, estimate the number of its irreducible components …