Back to Search
Start Over
THE SYZYGIES OF SOME THICKENINGS OF DETERMINANTAL VARIETIES.
- Source :
- Proceedings of the American Mathematical Society; Jan2017, Vol. 145 Issue 1, p49-59, 11p
- Publication Year :
- 2017
-
Abstract
- The vector space of m x n complex matrices (m ⩾ n) admits a natural action of the group GL=GL<subscript>m</subscript> xGL<subscript>n</subscript> via row and column operations. For positive integers a, b, we consider the ideal Iaxb defined as the smallest GL-equivariant ideal containing the b-th powers of the a x a minors of the generic m x n matrix. We compute the syzygies of the ideals Iaxb for all a, b, together with their GL-equivariant structure, generalizing earlier results of Lascoux for the ideals of minors (b=1) and of Akin-Buchsbaum-Weyman for the powers of the ideals of maximal minors (a=n). Our methods rely on a nice connection between commutative algebra and the representation theory of the superalgebra gl(mǀn), as well as on our previous calculation of Ext modules done in the context of describing local cohomology with determinantal support. Our results constitute an important ingredient in the proof by Nagpal-Sam-Snowden of the first non-trivial Noetherianity results for twisted commutative algebras which are not generated in degree one. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 145
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 125282751
- Full Text :
- https://doi.org/10.1090/proc/13197