복소기하학연구단
Speaker Minseong Kwon KAIST This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the first talk, I discussed the definition of an integrable G-structure and introduced the existence theorem for the structure tensor. In this talk, I will construct the structure tensor of a …
Speaker Minseong Kwon KAIST This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the previous two talks, we discussed the definition of the k-th order structure tensor of a G-structure. In the third talk, we will discuss how the structure tensors can be characterized …
Speaker Sangbum Yoo Gongju National University of Education Spectral data for Higgs bundles over a smooth curve has been studied by several mathematicians. The studies in this direction are originated by N.J.Hitchin. Specially, it has contributed to the studies on the fibers of the Hitchin map. In this talk, I will introduce spectral …
Speaker Seung-Jo Jung Jeonbuk National University Recently Mustata-Popa introduced a generalisation of multiplier ideals, which is called Hodge ideals. This talk introduces the Hodge ideals and explains the relations with other invariants, e.g. Bernstein-Sato polynomials, Hodge spectra, log canonical thresholds, minimal exponents etc. Mainly this talk concerns the relation between Hodge ideals and …
Speaker Hyungryul Baik KAIST For a tower of finite normal covers of graphs or surfaces, one can consider a sequence of metrics on the base given by pull-back of canonical metric of the covers. We show that such a sequence has a limit and it depends only on the cover approximated by the …
Speaker Sungmin Yoo IBS, Center for Complex Geometry A study on the positive variation of Kähler-Einstein metrics is first developed by Schumacher. More precisely, he has proved that the fiberwise Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive-definite on the total space. Later, Berman constructed the fiberwise Kähler-Ricci …
Speaker Sungmin Yoo IBS, Center for Complex Geometry After Yau suggested the problem of approximations of Kähler-Einstein metrics by Bergman type metrics, various types of Bergman metrics have been developed and studied by Tian, Donaldson, Tsuji, etc. They showed that if a polarized manifold admits a Kähler-Einstein metric, there exist a sequence of …
Speaker Qifeng Li IBS, Center for Complex Geometry For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification X, which is a smooth Fano variety of Picard number n enjoying many interesting properties. In this talk, we will show …
Speaker Seungjae Lee IBS, Center for Complex Geometry Let Γ be a cocompact torsion-free lattice in the automorphism group of complex unit ball Bn, Aut(Bn). In this talk, we discuss the existence of symmetric differentials on the compact ball quotient Σ = Bn / Γ. Since Σ has a Kähler metric induced by …
Speaker Seungjae Lee IBS, Center for Complex Geometry As the continuation of the previous talk, I discuss an L2 extension problem of holomorphic jets on compact complex hyperbolic forms. Let Γ be a cocompact torsion-free lattice in the automorphism group Aut(Bn) and Ω be a quotient Bn × Bn given by diagonal action …
Speaker Hosung Kim IBS, Center for Complex Geometry In 1979, the work of Mori had brought out the importance of the study of rational curves in higher-dimensional geometry. In 1990s, applying Mori's bend-and-break method, Campana and Kollar-Miyaoka-Mori proved that any Fano manifold is rationally connected. Since then the family of raional curves on …
Speaker Jeong-Seop Kim KAIST For a stable vector bundle E on a smooth projective curve, it is known that the symmetric powers Sk E are semi-stable and are stable for all k > 0 in sufficiently general. Moreover, if E has rank 2, then Sk E is destabilized by a line subbundle if …