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Projectable Veronese varieties

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Abstract

Let X be a non degenerate, reduced, reducible algebraic variety embedded in ℙN, of pure dimension m≥3. X is said to be an x-projectable Veronese variety if, assuming N≥m+x+1, X is of minimal degree, connected in codimension 1 and isomorphically projectable into a linear space of dimension m+x.

In this paper we classify 2 and 3-projectable Veronese varieties and x-projectable Veronese varieties having only linear components.

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Authors and Affiliations

  1. Dipartimento di Matematica, Univ. di Milano, via C. Saldini 50, 20133, Milano, Italy

    Alberto Alzati

  2. Dipartimento di Matematica, Univ. di Trento, via Sommarive 14, 38050, Povo, Italy

    Edoardo Ballico

Authors
  1. Alberto Alzati
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  2. Edoardo Ballico
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Corresponding author

Correspondence to Alberto Alzati.

Additional information

This work is within the framework of the national research projects: “Geometry on Algebraic Varieties” Cofin 2008 of MIUR and “Geometric Properties of Real and Complex Varieties” Cofin 2007 of MIUR.

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Alzati, A., Ballico, E. Projectable Veronese varieties. Rev Mat Complut 24, 219–249 (2011). https://doi.org/10.1007/s13163-010-0040-9

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  • DOI: https://doi.org/10.1007/s13163-010-0040-9

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