Asymptotic syzygies of algebraic varieties

被引：0
作者：
Lawrence Ein
Robert Lazarsfeld
机构：
[1] University Illinois at Chicago,Department of Mathematics
[2] University of Michigan,Department of Mathematics
来源：
Inventiones mathematicae | 2012年 / 190卷
关键词：
Vector Bundle; Algebraic Variety; Smooth Projective Variety; Ample Divisor; Segre Variety;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo–Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal.
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页码：603 / 646
页数：43
相关论文
共 37 条
[1]  
Aprodu M.(2004)Green–Lazarsfeld gonality conjecture for a generic curve of odd genus Int. Math. Res. Not. 63 3409-3416
[2]  
Aprodu M.(2003)Green–Lazarsfeld’s conjecture for generic curves of large gonality C. R. Math. Acad. Sci. Paris 336 335-339
[3]  
Voisin C.(1973)Canonical models of surfaces of general type Publ. Math. IHÉS 42 171-219
[4]  
Bombieri E.(2011)Koszul homology and syzygies of Veronese subalgebras Math. Ann. 351 761-779
[5]  
Bruns W.(1893)Sui multipli di uni serie lineare di gruppi di punti apparetmenente as una curva algebrica Rend. Circ. Mat. Palermo 7 99-119
[6]  
Conca A.(1981)Babbage’s conjecture, contact of surfaces, symmetric determinantal varieties and applications Invent. Math. 63 433-465
[7]  
Römer T.(1993)Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension Invent. Math. 111 51-67
[8]  
Castelnuovo G.(2005)Restricting linear syzygies: algebra and geometry Compos. Math. 141 1460-1478
[9]  
Catanese F.(2009)Betti numbers of graded modules and cohomology of vector bundles J. Am. Math. Soc. 22 859-888
[10]  
Ein L.(1984)Koszul cohomology and the geometry of projective varieties J. Differ. Geom. 19 125-171
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