복소기하학연구단
Speaker Junho Choe KIAS Castelnuovo-Mumford regularity, simply regularity, is one of the most interesting invariants in projective algebraic geometry, and the regularity conjecture due to Eisenbud and Goto says that the regularity can be controlled by the degree for any projective variety. But counterexamples to the conjecture have been constructed by some methods. …
Speaker Joaquín Moraga UCLA In this talk, we will introduce the absolute coregularity of Fano varieties. The coregularity measures the singularities of the anti-pluricanonical sections. Philosophically, most Fano varieties have coregularity 0. In the talk, we will explain some theorems that support this philosophy. We will show that a Fano variety of coregularity …
Speaker Andrea Petracci Università di Bologna Fano varieties are algebraic varieties with positive curvature; they are basic building blocks of algebraic varieties. Great progress has been recently made by Xu et al. to construct moduli spaces of Fano varieties by using K-stability (which is related to the existence of Kähler-Einstein metrics). These moduli …
Speaker JongHae Keum KIAS Fake projective planes (abbreviated as FPPs) are 2-dimensional complex manifolds with the same Betti numbers as the projective plane, but not isomorphic to it. FPPs can be uniformized by a complex 2-ball. In other words, they are ball quotients having the minimum possible Betti numbers. The existence of such …
Speaker JongHae Keum KIAS Fake projective planes (abbreviated as FPPs) are 2-dimensional complex manifolds with the same Betti numbers as the projective plane, but not isomorphic to it. FPPs can be uniformized by a complex 2-ball. In other words, they are ball quotients having the minimum possible Betti numbers. The existence of such …
Speaker Kangjin Han DGIST Secant variety (or more generally Join) construction is one of the main methods to construct a new geometric object from the original one in classical algebraic geometry. In this series of talks, we first consider some general facts on secant varieties and then focus on a specific topic, i.e. …
Speaker Kangjin Han DGIST Secant variety (or more generally Join) construction is one of the main methods to construct a new geometric object from the original one in classical algebraic geometry. In this series of talks, we first consider some general facts on secant varieties and then focus on a specific topic, i.e. …
Speaker Daniele Agostini Eberhard Karls Universität Tübingen The syzygies of a curve are the algebraic relation amongst the equation defining it. They are an algebraic concept but they have surprising applications to geometry. For example, the Green-Lazarsfeld secant conjecture predicts that the syzygies of a curve of sufficiently high degree are controlled by …
Speaker Yoon-Joo Kim MPI-Bonn A compact hyper-Kähler (HK) manifold and its Lagrangian fibration are higher-dimensional generalizations of a K3 surface and its elliptic fibration. A Lagrangian fibration f : X → B of a HK manifold is called isotrivial if its smooth fibers are all isomorphic to each other; this is the most …
Speaker Giancarlo Urzua UC Chille (This is a part of Seminars on Algebraic Surfaces and Related Topics.) I will introduce N-resolutions, which are the negative analog of the Kollár--Shepherd-Barron (1988) P-resolutions of a 2-dimensional cyclic quotient singularity. (We instead work with the corresponding M-resolutions of Benkhe-Christophersen (1994).) I will start by describing an …
Speaker Guolei Zhong IBS CCG (This is a part of Seminars on Algebraic Surfaces and Related Topics.) A vector bundle over a projective manifold is said to be pseudo-effective if the tautological line bundle of its Grothendieck projectivization is pseudo-effective. In this talk, I will show that a smooth non-uniruled projective surface S …
Speaker Yonghwa Cho IBS CCG (This is a part of Seminars on Algebraic Surfaces and Related Topics.) In this talk, I will explain how to associate a nodal surface in P3 with a cubic hypersurface, generalizing the method by Togliatti who constructed quintics with 31 nodes via a discriminant of a nodal cubic …