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Connected monomial invariants

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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 [C]: if Z is an integral variety of codimension two, satisfying the hypothesis s Z =sΓ, then its monomial invariants are connected.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, Italy

    Alberto Alzati & Alfonso Tortora

Authors
  1. Alberto Alzati
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  2. Alfonso Tortora
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Corresponding author

Correspondence to Alberto Alzati.

Additional information

The authors are members of CNR–GNSAGA (Italy).

During the preparation of this paper the authors were partially supported by National Research Project “Geometria sulle varietà algebriche COFIN 2002” of MIUR–Italy.

Mathematics Subject Classification (2001): 14M07

Acknowledgement The authors had fruitful discussions–either in person or via e-mail–on the topics of this paper with many people, among them Matsumi Amasaki, Iustin Coanda, Wolfram Decker, Mark Green, Francesco Russo, Enrico Sbarra, Enrico Schlesinger, Frank Schreyer; their help is gratefully acknowleged. Last, but by no means least, one of the referees pointed out that our original result, Corollary 2.7, could be significantly enlarged in its scope, thus giving Theorem 2.4.

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Alzati, A., Tortora, A. Connected monomial invariants. manuscripta math. 116, 125–133 (2005). https://doi.org/10.1007/s00229-004-0522-5

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  • DOI: https://doi.org/10.1007/s00229-004-0522-5

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