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A note on deformations of regular embeddings

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An Erratum to this article was published on 03 April 2017

Abstract

In this paper we give a description of the first order deformation space of a regular embedding \(X\hookrightarrow Y\) of reduced algebraic schemes. We compare our result with results of Ran (in particular, Deformation of Maps, Algebraic Curves and Projective Geometry (Trento, 1988), 246–253, Lecture Notes in Math, vol. 1389. Springer, Berlin, 1989, Prop. 1.3).

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Acknowledgments

We express deep gratitude to E. Sernesi for useful discussions on the subject of this paper. We also benefited from conversations with M. Lehn and M. Kemeny. Finally we would like to thank the referee for his detailed report. The first three authors have been supported by the GNSAGA of Indam and by the PRIN Project “Geometry of projective varieties”, funded by the Italian MIUR.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00173, Roma, Italy

    C. Ciliberto & F. Flamini

  2. Dipartimento di Matematica, Università della Calabria, via P. Bucci, cubo 31B, 87036, Arcavacata di Rende, CS, Italy

    C. Galati

  3. Department of Mathematics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    A. L. Knutsen

Authors
  1. C. Ciliberto
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  2. F. Flamini
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  3. C. Galati
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  4. A. L. Knutsen
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Corresponding author

Correspondence to C. Galati.

Additional information

This paper is dedicated to Philippe Ellia on the occasion of his sixtieth birthday.

An erratum to this article is available at http://dx.doi.org/10.1007/s12215-017-0307-9.

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Ciliberto, C., Flamini, F., Galati, C. et al. A note on deformations of regular embeddings. Rend. Circ. Mat. Palermo, II. Ser 66, 53–63 (2017). https://doi.org/10.1007/s12215-016-0276-4

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  • DOI: https://doi.org/10.1007/s12215-016-0276-4

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