복소기하학연구단
Speaker Jinhyun Park KAIST The classical reciprocity theorem, also called the residue theorem, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem. There is a different …
Speaker Jaewoo Jeong IBS CCG The Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017, …
Speaker Livia Campo KIAS The classification of terminal Fano 3-folds has been tackled from different directions: for instance, using the Minimal Model Program, via explicit Birational Geometry, and via Graded Rings methods. In this talk I would like to introduce the Graded Ring Database - an upper bound to the numerics of Fano …
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 Dennis The UiT The Arctic University of Norway Generic rank 2 distributions on 5-manifolds, i.e. "(2,3,5)-distributions", are interesting geometric structures arising in the study of non-holonomic systems, underdetermined ODE of Monge type, conformal 5-manifolds with special holonomy, etc. The origins of their study date to Élie Cartan's "5-variables" paper of 1910, where …
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 …