복소기하학연구단
Speaker Hosung Kim IBS CCG (This is a part of Seminars on Algebraic Surfaces and Related Topics.) The cotangent bundle of a complex projective manifold carries a natural holomorphic symplectic 2-form. The existence of a natural Lagrangian fibration structure of these non-compact complex manifolds has not been studied very much. In this talk, …
Speaker Dongsoo Shin Chungnam National U. (This is a part of Seminars on Algebraic Surfaces and Related Topics.) We investigate the correspondence between three theories of deformations of rational surface singularities: de Jong and van Straten's picture deformations, Kollár's P-resolutions, and Pinkham's smoothings of negative weights. We provide an explicit method for obtaining, …
Speaker JongHae Keum KIAS (This is a part of Seminars on Algebraic Surfaces and Related Topics.) The Cox ring of a variety is the total coordinate ring, i.e., the direct sum of all spaces of global sections of all divisors. When this ring is finitely generated, the variety is called Mori dream (MD). …
Speaker Junyan Zhao University of Illinois Chicago A general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X5 as a divisor of class -2KX5. This embedding is unique up to the action of the symmetric group S5. Taking a double cover of X5 branched along C yields …
Speaker Shigeru Mukai RIMS, Kyoto University PDF file
Speaker Shigeru Mukai RIMS, Kyoto University PDF file
Speaker Shigeru Mukai RIMS, Kyoto University PDF file
Speaker Changho Han University of Waterloo To construct a moduli space which is itself a compactification of a given moduli space, one needs to enlarge the class of objects in consideration (e.g. adding certain singular curves to the class of smooth curves). After a brief review of the compactifications of the moduli of …
Speaker Sung Gi Park Harvard University In this talk, I will discuss the behavior of positivity, hyperbolicity, and Kodaira dimension under smooth morphisms of complex quasi-projective manifolds. This includes a vast generalization of a classical result: a fibration from a projective surface of non-negative Kodaira dimension to a projective line has at least …
Speaker Shinnosuke Okawa Osaka University Semiorthogonal decomposition (SOD) is a central notion in the study of triangulated categories. In particular, SODs of the bounded derived category of coherent sheaves of a variety (SODs of the variety, for short) have profound relations to its geometry. In this talk I discuss the moduli functor which …
Speaker Shinnosuke Okawa Osaka University Motivated by the DK hypothesis, some years ago I proved that SODs of the derived category of a smooth projective variety are strongly constrained by the base locus of the canonical linear system. In particular, this leads to the indecomposability of the derived category of varieties whose canonical …
Speaker Chang-Yeon Chough Sogang Univ. This is an 8 hours long lecture series on algebraic stacks, which have become an important part of algebraic geometry (for example, in the study of moduli spaces) since Deligne and Mumford established the foundation of the theory of stacks. This crash course will be following roughly "Algebraic …