Vol. 10, No. 4, 2016

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Interpolation for restricted tangent bundles of general curves

Eric Larson

Vol. 10 (2016), No. 4, 931–938
DOI: 10.2140/ant.2016.10.931

Let q1,q2,,qn r be a general collection of points, and (C,p1,p2,,pn) a general marked curve of genus g. We determine when there exists a nondegenerate degree-d map f : C r such that f(pi) = qi for all i. This is a consequence of our main theorem, which states that the restricted tangent bundle fTr of a general curve of genus g, equipped with a general degree-d map f to r, satisfies the property of interpolation, i.e., that for a general effective divisor D of any degree on C, either H0(fTr(D)) = 0 or H1(fTr(D)) = 0. We also prove an analogous theorem for the twist fTr(1).

restricted tangent bundle, interpolation
Mathematical Subject Classification 2010
Primary: 14H99
Received: 30 November 2015
Accepted: 16 May 2016
Published: 20 June 2016
Eric Larson
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States