복소기하학연구단
Speaker Shin-Young Kim IBS-CGP We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents. In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves. We relate these …
Speaker Qifeng Li Shandong University To each complex composition algebra A, there associates a projective symmetric manifold X(A) of Picard number 1. The vareity X(A) is closed related with Freudenthal's Magic Square, which is a square starting from the adjiont varieties of F4, E6, E7 and E8. In a recent joint work with …
Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain …
Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain …
Speaker Minseong Kwon KAIST For each rational homogeneous space, the space of lines is now well-understood and can be described in terms of the induced group action. It is natural to consider rational curves of higher degree, and in this talk, we discuss geometry of conics in adjoint varieties, which are rational homogeneous …
Speaker Kyeong-Dong Park Gyeongsang National University The aim of this seminar is to provide participants with a comprehensive understanding of the paper "K-stability of Fano spherical varieties" by Thibaut Delcroix. For a reductive algebraic group G, a normal G-variety is called spherical if it contains an open B-orbit, where B is a fixed …
Speaker Kyeong-Dong Park Gyeongsang National University The aim of this seminar is to provide participants with a comprehensive understanding of the paper "K-stability of Fano spherical varieties" by Thibaut Delcroix. For a reductive algebraic group G, a normal G-variety is called spherical if it contains an open B-orbit, where B is a fixed …
Speaker Kyeong-Dong Park Gyeongsang National University The aim of this seminar is to provide participants with a comprehensive understanding of the paper "K-stability of Fano spherical varieties" by Thibaut Delcroix. For a reductive algebraic group G, a normal G-variety is called spherical if it contains an open B-orbit, where B is a fixed …
Speaker George Hitching Oslo Metropolitan University Let C be a smooth projective curve of genus g. The symplectic Brill-Noether locus S(k, 2n, K) parametrises stable bundles of rank 2n over C with at least k independent sections, and which admit a nondegenerate skewsymmetric bilinear form with values in the canonical bundle K. This …
Speaker Thomas Peternell University of Bayreuth Given a projective complex manifold M with an ample polarization there is canonically associated an affine bundle Z over M. The question I will discuss is under which circumstances Z is an affine variety, or at least Stein. This is related to the global structure of M, …
Speaker Yum-Tong Siu Harvard University For sums of squares of real vector fields, Hörmander linked subelliptic estimates to the spanning property of iterated Lie brackets of vector fields. Kohn studied the more complicated analogue of subelliptic ∂ estimates for weakly pseudoconvex domains, with vector-valued unknowns. In the weak-solution approach to solving the ∂ …
Speaker Fabrizio Catanese University of Bayreuth We consider the geometric map C, called Cayleyan, associating to a plane cubic E the adjoint of its dual curve. We show that C and the classical Hessian map H generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps, and …