The Severi bound on sections of rank two semistable bundles on a Riemann surface

@inproceedings{Cilleruelo2001TheSB,
  title={The Severi bound on sections of rank two semistable bundles on a Riemann surface},
  author={Javier Cilleruelo and Ignacio Sols},
  year={2001}
}
Let E be a semistable, rank two vector bundle of degree d on a Riemann surface C of genus g > 1, i.e. such that the minimal degree s of a tensor product of E with a line bundle having a nonzero section is nonnegative. We give an analogue of Clifford's lemma by showing that E has at most (ds)/2 + 6 independent sections, where 6 is 2 or 1 according to whether the Krawtchouk polynomial Kr(n, N) is zero or not at r = (ds)/2 + 1, n = g, N = 2g-s (the analogous bound for nonsemistable rank two… CONTINUE READING

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