Syzygies of bounded rank symmetric tensors are generated in bounded degree

2015/10/31 by Steven V Sam · 1 citation
Mathematics · #math.AC #math.AG #math.RA #msc:13D02 #msc:13E05 #msc:14M99 #msc:15A69 #msc:16T15

paper · pdf · doi:10.1007/s00222-016-0668-2

published as Math. Ann. 368 (2017), no. 3, 1095-1108 · 11 pages; v2: expanded exposition

arxiv created 2017/01/06 · arxiv updated 2017/07/25

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.

Cited by

• Syzygies of secant ideals of Plücker-embedded Grassmannians are generated in bounded degree

Related

• Syzygies of secant ideals of Plücker-embedded Grassmannians are generated in bounded degree
• A duality theorem for syzygies of Veronese ideals
• Bounds for degrees of syzygies of polynomials defining a grade two ideal
• Syzygies of the Veronese modules
• Asymptotic syzygies of algebraic varieties