복소기하학연구단
Speaker Han-Bom Moon Fordham University An Ulrich bundle is a vector bundle with very strong cohomology vanishing conditions. Eisenbud and Schreyer conjectured that every smooth projective variety possesses an Ulrich bundle. Despite many results on low dimensional varieties and special varieties, the general existence is unknown. In this talk, I will describe recent …
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 …
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 …
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 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 Minseong Kwon Gyeongsang National University In the 1970s, Demazure studied the automorphism groups of two types of almost homogeneous varieties: rational homogeneous spaces and toric varieties. Especially, for a smooth complete toric variety, Demazure obtained a structure theorem for the connected automorphism group in terms of the so-called Demazure roots. In this …
Speaker Gebhard Martin University of Bonn The automorphism group of a general Enriques surface is the 2-congruence subgroup of the Weyl group of the E10-lattice. In particular, it is infinite and not virtually solvable. On the other end of the spectrum, there do exist Enriques surfaces with finite automorphism group, first classified over …
Speaker Kyoung-Seog Lee POSTECH Intersections of two quadrics form an interesting class of algebraic varieties and they have been intensively studied from various aspects. In these talks, I will discuss these various aspects of the intersection of two quadrics and how to interpret/generalize some of the classical algebraic geometry results using the derived …
Speaker Kyoung-Seog Lee POSTECH Intersections of two quadrics form an interesting class of algebraic varieties and they have been intensively studied from various aspects. In these talks, I will discuss these various aspects of the intersection of two quadrics and how to interpret/generalize some of the classical algebraic geometry results using the derived …