Abstract
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.
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Communicated by: I. Coskun
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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.
Acknowledgements
The author wants to gratefully acknowledge all the people who helped him during the preparation of this paper: in particular S. Boissière and A. Sarti who suggested the problem from which the present paper originated, and C. Ciliberto, F. Flamini and A. Lanteri for useful comments on the subject and suggestions during the writing. He also wants to thank the referee for his/her suggestions, which led to a substantial improvement of the first version of this paper.
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