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Advances in Geometry

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The degree of the tangent and secant variety to a projective surface

Andrea Cattaneo
  • Corresponding author
  • Institut Camille Jordan UMR 5208, Université Claude Bernard Lyon 1, 69622, Villeurbanne Cedex, France
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Published Online: 2019-06-30 | DOI: https://doi.org/10.1515/advgeom-2019-0015


We present a way of computing the degree of the secant (resp. tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is 3-very ample. This method exploits the link between these varieties and the Hilbert scheme 0-dimensional subschemes of length 2 of the surface.

Keywords: Hilbert scheme; degree of secant variety; degree of tangent variety

MSC 2010: Primary 14J28; 14N15


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About the article

Received: 2017-05-24

Revised: 2018-02-20

Revised: 2018-09-17

Revised: 2019-04-08

Published Online: 2019-06-30

Funding: The author is supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) and is member of GNSAGA of INdAM. The main parts of this paper were written while the author was granted a research fellowship by Università degli Studi dell’Insubria in Como.

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0015.

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