Abstract
We completely describe the Fano scheme of lines \(\mathbf {F}_1(X)\) for a projective toric surface X in terms of the geometry of the corresponding lattice polygon.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barth, W., Van de Ven, A.: Fano varieties of lines on hypersurfaces. Arch. Math. (Basel), 31(1):96–104 (1978/79)
Beheshti, R.: Lines on projective hypersurfaces. J. Reine Angew. Math. 592, 1–21 (2006)
Eisenbud, D., Harris, J.: The geometry of schemes. Graduate Texts in Mathematics, vol. 197. Springer-Verlag, New York (2000)
Fulton, W.: Introduction to toric varieties, volume 131 of Annals of Mathematics Studies. The William H. Roever Lectures in Geometry. Princeton University Press, Princeton (1993)
Harris, J., Mazur, B., Pandharipande, R.: Hypersurfaces of low degree. Duke Math. J. 95(1), 125–160 (1998)
Hartshorne, R.: Algebraic geometry. Graduate texts in mathematics, No. 52. Springer-Verlag, New York (1977)
Ito, A.: Algebro-geometric characterization of Cayley polytopes. Adv. Math. 270, 598–608 (2015)
Acknowledgments
We thank Andreas Hochenegger for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ilten, N. Fano schemes of lines on toric surfaces. Beitr Algebra Geom 57, 751–763 (2016). https://doi.org/10.1007/s13366-016-0294-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13366-016-0294-6