Curves with a node in projective spaces with good postulation

Abstract

Fix integers d, g, r such that r ≥ 3, g > 0 and d ≥ g + r. Here we prove the existence of an integral non-special curve C in an r-dimensional projective space such that deg(C) = d, pa(C) = g, C has exactly one node and C has maximal rank (i.e. it has the expected postulation), i.e., the general non-special embedding of a general curve with a single node has maximal rank. M.S.C. 2010: 14H51, 4N05.

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