Laplace Equations and the Weak Lefschetz Property
نویسندگان
چکیده
منابع مشابه
The Strength of the Weak Lefschetz Property
We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative a...
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In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. 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 t...
متن کاملInverse systems, Gelfand-Tsetlin patterns and the weak Lefschetz property
In [19], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x 1 ,. .. , 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 [24]. 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 connec...
متن کاملSyzygy Bundles on P and the Weak Lefschetz Property
Let K be an algebraically closed field of characteristic zero and let I = (f1, . . . , fn) be a homogeneous R+-primary ideal in R := K[X, Y, Z]. If the corresponding syzygy bundle Syz(f1, . . . , fn) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we...
متن کاملMonomial Ideals, Almost Complete Intersections and the Weak Lefschetz Property
has maximal rank, i.e. it is injective or surjective. In this case, the linear form L is called a Lefschetz element of A. (We will often abuse notation and say that the corresponding ideal has the WLP.) The Lefschetz elements of A form a Zariski open, possibly empty, subset of (A)1. Part of the great interest in the WLP stems from the fact that its presence puts severe constraints on the possib...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2013
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2012-033-x