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AbstractWe give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.
CitationLubbes, N. (2019). A degree bound for families of rational curves on surfaces. Journal of Pure and Applied Algebra, 223(1), 30–47. doi:10.1016/j.jpaa.2018.02.033
SponsorsI would like to thank Josef Schicho for useful discussions. This work was supported by base funding of the King Abdullah University of Science and Technology.