We define the monomial invariants of a projective variety Z; they are invariants coming from the generic initial ideal of Z. We prove that, under suitable hypotheses, a variety of codimension at least two has connected monomial invariants; as a corollary, we generalize a result of Cook: if Z is an integral variety of codimension two, satisfying some assumptions on the minimal degree of a hypersurface containing it, then its invariants are connected.
Connected monomial invariants / A. Alzati, A. Tortora. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 116:2(2005 Feb 02), pp. 125-133.
Connected monomial invariants
A. AlzatiPrimo
;A. TortoraUltimo
2005
Abstract
We define the monomial invariants of a projective variety Z; they are invariants coming from the generic initial ideal of Z. We prove that, under suitable hypotheses, a variety of codimension at least two has connected monomial invariants; as a corollary, we generalize a result of Cook: if Z is an integral variety of codimension two, satisfying some assumptions on the minimal degree of a hypersurface containing it, then its invariants are connected.
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