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Algebraic Geometry Seminar - Euisung Park(KOREA UNIVERSITY)

posted Mar 25, 2012, 6:29 PM by Jihye Jung   [ updated Mar 25, 2012, 6:40 PM ]
 - 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
 - Abstracts
    : 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.