Singularities and syzygies of secant varieties of nonsingular projective curves

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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.
Publisher
SPRINGER HEIDELBERG
Issue Date
2020-11
Language
English
Article Type
Article
Citation

INVENTIONES MATHEMATICAE, v.222, no.2, pp.615 - 665

ISSN
0020-9910
DOI
10.1007/s00222-020-00976-5
URI
http://hdl.handle.net/10203/295154
Appears in Collection
MA-Journal Papers(저널논문)
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