3x3 Minors of Catalecticants
Abstract
Secant varieties to Veronese embeddings of projective space are classical varieties whose equations are not completely understood. Minors of catalecticant matrices furnish some of their equations, and in some situations even generate their ideals. Geramita conjectured that this is the case for the secant line variety of the Veronese variety, namely that its ideal is generated by the 3x3 minors of any of the "middle" catalecticants. Part of this conjecture is the statement that the ideals of 3x3 minors are equal for most catalecticants, and this was known to hold settheoretically. We prove the equality of 3x3 minors and derive Geramita's conjecture as a consequence of previous work by Kanev.
 Publication:

arXiv eprints
 Pub Date:
 November 2010
 arXiv:
 arXiv:1011.1564
 Bibcode:
 2010arXiv1011.1564R
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 14M12
 EPrint:
 v3: minor changes, to appear in Mathematical Research Letters