Lattice polygons and families of curves on rational surfaces
Niels Lubbes
and Josef Schicho
DOI: 10.1007/s10801-010-0268-y
Abstract
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational complex projective surfaces.
Pages: 213–236
Keywords: keywords algebraic geometry; toric geometry; lattice polygons; families of curves; surfaces
Full Text: PDF
References
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2. Draisma, J., McAllister, T.B., Nill B.: Lattice width directions and Minkowski's 3d -theorem. Technical Report, arXiv:[math.CO] (2009)
3. Günter, Ewald: Combinatorial Convexity and Algebraic Geometry. Graduate Texts in Mathematics, vol.
168. Springer, New York (1996). ISBN 0-387-94755-8
4. Fulton, W.: Introduction to Toric Varieties. Annals of Mathematics Studies, vol.
131. Princeton University Press, Princeton (1993)
5. Haase, C., Schicho, J.: Lattice polygons and the number 2i +
7. Math. Mon. (2009)
6. Halphen, G.H.: On plane curves of degree six through nine double points (in french). Bull. Soc. Math. Fr. 10, 162-172 (1882)
7. Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, vol.
52. Springer, New York (1977). J Algebr Comb (2011) 34:213-236
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