복소기하학연구단
Speaker Fabrizio Catanese University of Bayreuth We consider the geometric map C, called Cayleyan, associating to a plane cubic E the adjoint of its dual curve. We show that C and the classical Hessian map H generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps, and …
Speaker Seung uk Jang Université de Rennes 1 We discuss the algebraic dynamics on Markov cubics generated by Vieta involutions, in the tropicalized setting, including some introduction to the tropicalization. It turns out that there is an invariant subset of the tropicalized Markov cubic where the action by Vieta involutions can be modeled …
Speaker Yaoxiong Wen KIAS During this presentation, I will discuss the generalized quiver mutation conjecture proposed by Prof. Ruan. Our focus will be on proving this conjecture for the Grassmannian bundle. Additionally, we will explore the determinantal variety and its two different desingularizations, known as PAX/PAXY models. We will demonstrate the relationship between …
Speaker Guolei Zhong IBS-CCG In this talk, we discuss the structure of projective varieties with certain positive tangent sheaves. More precisely, when the tangent sheaf is almost nef or positively curved, we construct a well-defined MRC fibration and study the Fujita decomposition of reflexive sheaves. Besides, we show that the almost nefness of …
Speaker Gil Bor CIMAT Place a point light source inside a smooth convex billiard table (or mirror). The n-th caustic by reflection is the envelope of light rays after n reflections. Theorem: each of these caustics, for a generic point light source, has at least 4 cusps. Conjecture: there are exactly 4 cusps …
Speaker Gil Bor CIMAT At first sight, the pair of front and back wheel tracks left by a passing bike on a sandy or muddy terrain seems like a random pair of curves. This is not the case. For example, one can usually distinguish between the front and back wheel tracks, and even …
Speaker Yotsutani Naoto Kagawa University In 2001, Donaldson proved that if a polarized manifold (X, L) admits constant scalar curvature Kähler metrics in c1(L), then (X, L) is asymptotically Chow stable whenever its automorphism group Aut(X, L) is discrete. In this talk, we show that this result does not hold in the case …
Speaker Seungjae Lee IBS CCG In this talk, we investigate the L2-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. As a result, we establish a version of L2-Hodge decompostion for complex hyperbolic space forms with finite volume, under some mild …
Speaker Andreas Höring University of Nice Symmetric holomorphic forms on projective manifolds have been studied from various angles in the last ten years : Brotbek-Darondeau and independently Song-Yan Xie have shown that complete intersections of sufficiently high degree and codimension have an ample cotangent bundle, so many symmetric forms. Vice versa Campana and …
Speaker Andreas Höring University of Nice Symmetric holomorphic forms on projective manifolds have been studied from various angles in the last ten years : Brotbek-Darondeau and independently Song-Yan Xie have shown that complete intersections of sufficiently high degree and codimension have an ample cotangent bundle, so many symmetric forms. Vice versa Campana and …
Speaker Liana Heuberger University of Bath I will discuss how to use the classification of Gorenstein canonical Fano polytopes (and Laurent polynomials supported on them) in the construction of terminal Q-factorial Fano threefolds which admit a toric degeneration. I contextualise this within the framework of Fano mirror symmetry, using a technique called Laurent …
Speaker Grzegorz Kapustka Jagiellonian University We describe a locally complete family of projective irreducible holomorphic symplectic orbifolds as double covers of special complete intersections (3, 4) in P6. This is a joint work with C. Camere, A. Garbagnati and M. Kapustka.