- Title: Projective subvarieties having large Green-Lazarsfeld index
- Speaker : Euisung Park(KOREA UNIVERSITY)
- Date & Time : Mar 16(Fri) , 2012 2:00~3:00 PM
- Place : Math Science building room 404
: Let X ½ Pr be a nondegenerate projective irreducible subvariety of degreed and codimension c ¸ 1.
The Green-Lazarsfeld index of X, denoted by index(X), is de¯ned as the largest p such that the
homogeneous ideal of X is generated by quadrics and the syzygies among them are generated by linear
syzygies until the (p¡1)-th stage. Thus index(X) is an important invariant in order to describe the minimal
free resolution of X. Recently it is shown that d = c+1 if and only if index(X) ¸ c, and X is a del Pezzo variety
if and only if index(X) = c ¡ 1.
In my talk, I will speak about the classi¯cation result of projective varieties satisfying the condition
index(X) = c¡2 and the condition index(X) = c¡3, respectively.