복소기하학연구단
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 …
Speaker Lucas Kaufmann IBS, Center for Complex Geometry The field of complex dynamics deals with the study of the iteration of a map from a complex manifold to itself. The one dimensional theory is more than one-hundred years old and is now very well developed. Due to the fundamental differences between complex analysis …
Speaker Lucas Kaufmann IBS, Center for Complex Geometry The study of functional equations is at the origin of the early developments of the iteration theory of polynomials and rational functions, carried out by Fatou, Julia, Ritt and others. Among these equations, the commutation relation f g = g f is particularly interesting. In …
Speaker Joonyeong Won KIAS We discuss on recent progresses of the existence problem of Kähler-Einstein metric on Fano varieties by K-stability of them and also the existence problem of Sasaki-Einstein metric on 5-dimensional Smale manifolds via K-stability of weighted hypersurface log del Pezzo surfaces.
Speaker Baohua Fu Chinese Academy of Science We propose a conjectural list of Fano manifolds of Picard number one whose normalized tangent bundle is pseudoeffective and we prove it in various situations by relating it to the complete divisibility conjecture of Russo and Zak on varieties with small codegrees. The pseudoeffective cone of …
Speaker Yong Hu KIAS For complex smooth irregular 3-folds of general type, I will introduce the optimal Noether-Severi inequality. This answers an open question of Zhi Jiang in dimension three. Moreover, I will also completely describe the canonical models of irregular 3-folds attaining the Noether-Severi equality. This is a joint work with Tong …
Speaker Sukmoon Huh Sungkyunkwan University A logarithmic sheaf is a sheaf of differential one-forms on a variety with logarithmic poles along a given divisor. One of the main problems on this object is to see whether Torelli property holds, i.e. whether two different divisors define two non-isomorphic logarithmic sheaves. In this talk, after …
Speaker Yonghwa Cho KIAS A (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat …
Speaker Jinhyung Park Sogang University There are several definitions of the "numerical" Iitaka dimensions of a pseudoeffective divisor, which are numerical analogues to the Iitaka dimension. Recently, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk, we prove that many of numerical Iitaka dimensions are equal to the …
Speaker Sung Rak Choi Yonsei University We will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct, we obtain a criterion of birational isotriviality in terms of Okounkov …