We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Ideals of bounded rank symmetric tensors are generated in bounded degree.
- Authors
Sam, Steven
- Abstract
Over a field of characteristic zero, we prove that for each r, there exists a constant C( r) so that the prime ideal of the rth secant variety of any Veronese embedding of any projective space is generated by polynomials of degree at most C( r). The main idea is to consider the coordinate ring of all of the ambient spaces of the Veronese embeddings at once by endowing it with the structure of a Hopf ring, and to show that its ideals are finitely generated. We also prove a similar statement for partial flag varieties and, in fact, arbitrary projective schemes, and we also get multi-graded versions of these results.
- Subjects
TENSORS of higher rank; BOUNDED arithmetics; SECANT function; GENERATORS of ideals (Algebra); VECTOR spaces
- Publication
Inventiones Mathematicae, 2017, Vol 207, Issue 1, p1
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-016-0668-2