Inverse systems, GelfandTsetlin patterns and the weak Lefschetz property
Abstract
MiglioreMiróRoigNagel [Trans. A.M.S. 2011, arXiv: 0811.1023] show that the weak Lefschetz property (WLP) can fail for an ideal I in K[x_1,x_2,x_3,x_4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x_1,x_2,x_3], where WLP always holds [H.Schenck, A.Seceleanu, Proc. A.M.S. 2010, arXiv:0911.0876]. We use the inverse system dictionary to connect I to an ideal of fat points and show that failure of WLP for powers of linear forms is connected to the geometry of the associated fat point scheme. Recent results of SturmfelsXu in [J. Eur. Math. Soc. 2010, arXiv:0803.0892] allow us to relate WLP to GelfandTsetlin patterns. See the paper "On the weak Lefschetz property for powers of linear forms" by MiglioreMiróRoigNagel [arXiv:1008.2149] for related results.
 Publication:

arXiv eprints
 Pub Date:
 August 2010
 DOI:
 10.48550/arXiv.1008.2377
 arXiv:
 arXiv:1008.2377
 Bibcode:
 2010arXiv1008.2377H
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry
 EPrint:
 to appear in J. London Math. Soc