복소기하학연구단
Speaker Jinhyung Park KAIST In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality gon(C) of a smooth projective curve C of genus g can be read off from weight-one syzygies of a sufficiently positive line bundle L, and also proposed possible least degree of L, that is 2g+gon(C)-1. In 2015, Ein-Lazarsfeld …
Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a …
Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a …
Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a …
Speaker Jie Liu AMSS I'll report joint works with Baohua Fu (AMSS), in which we investigate symplectic singularities arising from the affinization of the cotangent bundle of a smooth variety.
Speaker Meng Chen Fudan University In this talk, I will present a complete proof for the following theorem: the inequality K3 ≥ 4/3 pg-10/3 holds for all 3-folds of general type.
Speaker Meng Chen Fudan University In this lecture, I will report some new progress in studying moduli spaces of algebraic 3-folds with very small canonical volume.
Speaker JongHae Keum KIAS A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface. Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular. By the classification of surfaces, S is either …
Speaker Gian Pietro Pirola University of Pavia We present some computational improvements that allow us to study asymptotic lines in the tangent of the moduli space Mg of the curves of genus g. The asymptotic directions are those tangent directions that are annihilated by the second fundamental form induced by the Torelli map. …
Speaker Gian Pietro Pirola University of Pavia We study normal functions (sections of the Jacobian bundle) defined on the moduli space of pointed plane curves. Using the infinitesimal Griffiths invariant (refined by M. Green and C. Voisin) we show that a normal function with nontrivial but sufficiently "small" support cannot be "locally constant". …
Speaker Han-Bom Moon Fordham University An Ulrich bundle is a vector bundle with very strong cohomology vanishing conditions. Eisenbud and Schreyer conjectured that every smooth projective variety possesses an Ulrich bundle. Despite many results on low dimensional varieties and special varieties, the general existence is unknown. In this talk, I will describe recent …
Speaker Sung Gi Park Princeton U. / IAS The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge-Du …