Curves having one place at infinity and linear systems on rational surfaces

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• 作者：F. Monserrat
• 关键词：Updating ambiguous beliefs ; Full Bayesian Updating ; Choquet Expected Utility
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2007
• 出版时间：December 2007
• 年：2007
• 卷：211
• 期：3
• 页码：685-701
• 全文大小：481 K

文摘

Denoting by the linear system of plane curves of degree dbcaad4d3"" title=""Click to view the MathML source"">d passing through r+1 generic points p₀,p₁,…,p_r of the projective plane with multiplicity m_i (or larger) at each p_i, we prove the Harbourne–Hirschowitz Conjecture for linear systems determined by a wide family of systems of multiplicities and arbitrary degree d. Moreover, we provide an algorithm for computing a bound for the regularity of an arbitrary system , and we give its exact value when is in the above family. To do that, we prove an H¹-vanishing theorem for line bundles on surfaces associated with some pencils “at infinity”.