We study several properties of multihomogeneous prime ideals. We show that the multigraded generic initial ideal of a prime has very special properties, for instance, its radical is Cohen-Macaulay. We develop a comprehensive study of multidegrees in arbitrary positive multigraded settings. In these environments, we extend the notion of Cartwright-Sturmfels ideals by means of a standardization technique. Furthermore, we recover or extend important results in the literature, for instance: we provide a multidegree version of Hartshorne’s result stating the upper semicontinuity of arithmetic degree under flat degenerations, and we give an alternative proof of Brion’s result regarding multiplicity-free varieties.

Multidegrees, prime ideals, and non-standard gradings

Caminata A.;Conca A.
2023-01-01

Abstract

We study several properties of multihomogeneous prime ideals. We show that the multigraded generic initial ideal of a prime has very special properties, for instance, its radical is Cohen-Macaulay. We develop a comprehensive study of multidegrees in arbitrary positive multigraded settings. In these environments, we extend the notion of Cartwright-Sturmfels ideals by means of a standardization technique. Furthermore, we recover or extend important results in the literature, for instance: we provide a multidegree version of Hartshorne’s result stating the upper semicontinuity of arithmetic degree under flat degenerations, and we give an alternative proof of Brion’s result regarding multiplicity-free varieties.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1151737
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