Singularities and syzygies of secant varieties of nonsingular projective curves

被引:8
|
作者
Ein, Lawrence [1 ]
Niu, Wenbo [2 ]
Park, Jinhyung [3 ]
机构
[1] Univ Illinois, Dept Math, 851 South Morgan St, Chicago, IL 60607 USA
[2] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA
[3] Sogang Univ, Dept Math, 35 Beakbeom Ro, Seoul 04107, South Korea
关键词
KOSZUL COHOMOLOGY; GEOMETRY; REGULARITY; NORMALITY; EQUATIONS;
D O I
10.1007/s00222-020-00976-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies. The main results assert that if the degree of the embedding line bundle of a nonsingular curve of genusgis greater than 2g+2k+p for nonnegative integerskandp, then thek-th secant variety of the curve has normal Du Bois singularities, is arithmetically Cohen-Macaulay, and satisfies the property N-k+2,N-p. In addition, the singularities of the secant varieties are further classified according to the genus of the curve, and the Castelnuovo-Mumford regularities are also obtained as well. As one of the main technical ingredients, we establish a vanishing theorem on the Cartesian products of the curve, which may have independent interests and may find applications elsewhere.
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页码:615 / 665
页数:51
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