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### Algebraic Geometry Seminar - Jeaman Ahn(Kongju National University)

posted Apr 6, 2012, 12:22 AM by Jihye Jung   [ updated Apr 6, 2012, 12:23 AM ]
 - Title: ALGEBRAIC AND GEOMETRIC PROPERTIES OF PROJECTIVE SCHEMES WITH PROPERTY $\textbf{N}_{3, p}$  - Speaker : Jeaman Ahn(Kongju National University)  - Date & Time : April 6 (Fri) , 2012 14:00~  - Place : Math Science building room 404  - Abstract     : We investigate some algebraic and geometric properties of reduced closed subschemes with the condition $\textbf{N}_{3,p}, p\ge 1$. For property $\textbf{N}_{d,p}$, which is a slight generalization of property $\textbf{N}_p$ due to Green-Lazarsfeld, the interplay between linear syzygies of defining quadratic equations and geometric properties has been focused for a long time. However, not very much is actually known about varieties with the condition $\textbf{N}_{3,p}, p\ge 1$. Even though it is so delicate to treat those cases, we proceed to get information on linear sections, Castelnuovo normality, CM-regularity and multiple loci of projections according to moving the center of projection from the condition $\textbf{N}_{3,p}, p\ge 1$. We will also provide interesting examples which illuminate various theorems in this talk.