Bulletin of the Belgian Mathematical Society - Simon Stevin

On secant spaces to Enriques surfaces

Andreas Leopold Knutsen

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Abstract

We relate the minimal gonality of smooth curves in a complete, ample, base point free linear system $|L|$ on an Enriques surface to the existence of certain secant spaces on the image of the surface mapped by the adjoint system. We also explicitly compute the minimal gonality in terms of invariants of the line bundle $L$. In particular, we obtain a precise criterion for the variation of the gonality of the curves.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 5 (2009), 907-931.

Dates
First available in Project Euclid: 9 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1260369406

Digital Object Identifier
doi:10.36045/bbms/1260369406

Mathematical Reviews number (MathSciNet)
MR2574369

Zentralblatt MATH identifier
1204.14014

Subjects
Primary: 14H51: Special divisors (gonality, Brill-Noether theory) 14C20: Divisors, linear systems, invertible sheaves 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J05 14F17: Vanishing theorems [See also 32L20]

Keywords
Enriques surfaces line bundles curves gonality higher order embeddings

Citation

Knutsen, Andreas Leopold. On secant spaces to Enriques surfaces. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 5, 907--931. doi:10.36045/bbms/1260369406. https://projecteuclid.org/euclid.bbms/1260369406


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