The Weak Lefschetz Property, Inverse Systems and Fat Points
نویسنده
چکیده
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 the geometry of the associated fat point scheme.
منابع مشابه
Inverse 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...
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