2018/03/09 by Robert P. Laudone, Laudone, Robert P.
Mathematics · #13D02 #13E05 #14M15 #15A69 #16T15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.AG #math.RA #msc:13D02 #msc:13E05 #msc:14M15 #msc:15A69 #msc:16T15
paper · pdf · doi:10.48550/arxiv.1803.04259
25 pages; v2: corrected typos, expanded exposition. arXiv admin note: text overlap with arXiv:1510.04904 by other authors
arxiv created 2018/03/23 · arxiv updated 2018/03/28
Over a field of characteristic 0, we prove that for each r ≥ 0 there exists a constant C(r) so that the prime ideal of the rth secant variety of any Plücker-embedded Grassmannian \bf Gr(d,n) is generated by polynomials of degree at most C(r), where C(r) is independent of d and n. This bounded generation ultimately reduces to proving a poset is noetherian, we develop a new method to do this. We then translate the structure we develop to the language of functor categories to prove the ith syzygy module of the coordinate ring of the rth secant variety of any Plücker-embedded Grassmannian \bf Gr(d,n) is concentrated in degrees bounded by a constant C(i,r), which is again independent of d and n.