Mathematics – Algebraic Geometry
Scientific paper
2011-03-02
Mathematics
Algebraic Geometry
Sections renumbered to conform to published version. To appear in Invent. Math
Scientific paper
This paper studies the asymptotic behavior of the syzygies of a smooth projective variety X as the positivity of the embedding line bundle grows. We prove that as least as far as grading is concerned, the minimal resolution of the ideal of X has a surprisingly uniform asymptotic shape: roughly speaking, generators eventually appear in almost all degrees permitted by Castelnuovo-Mumford regularity. This suggests in particular that a widely-accepted intuition derived from the case of curves -- namely that syzygies become simpler as the degree of the embedding increases -- may have been misleading. For Veronese embeddings of projective space, we give an effective statement that in some cases is optimal, and conjecturally always is so. Finally, we propose a number of questions and open problems concerning asymptotic syzygies of higher-dimensional varieties.
Ein Lawrence
Lazarsfeld Robert
No associations
LandOfFree
Asymptotic syzygies of algebraic varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Asymptotic syzygies of algebraic varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic syzygies of algebraic varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-475274