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Syzygies of bounded rank symmetric tensors are generated in bounded degree

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Abstract

We study the syzygies of secant ideals of Veronese subrings of a fixed commutative graded algebra over a field of characteristic 0. One corollary is that the degrees of the minimal generators of the ith syzygy module of the coordinate ring of the rth secant variety of any Veronese embedding of a projective scheme X can be bounded by a constant that only depends on i, r, and X, and not on the choice of the Veronese embedding.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, USA

    Steven V Sam

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  1. Steven V Sam
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Correspondence to Steven V Sam.

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Communicated by Vasudevan Srinivas.

SS was partially supported by NSF DMS-1500069 and Iuventus Plus Grant 0301/IP3/2015/73 of the Polish Ministry of Science.

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Sam, S.V. Syzygies of bounded rank symmetric tensors are generated in bounded degree. Math. Ann. 368, 1095–1108 (2017). https://doi.org/10.1007/s00208-016-1509-8

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  • DOI: https://doi.org/10.1007/s00208-016-1509-8

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