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The monodromy of certain families of linear series is at least the alternating group


Author: Dan Edidin
Journal: Proc. Amer. Math. Soc. 113 (1991), 911-922
MSC: Primary 14H10; Secondary 14C20, 20B35
DOI: https://doi.org/10.1090/S0002-9939-1991-1069686-X
MathSciNet review: 1069686
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Abstract: Let $ g,r,d$ be positive integers such that the Brill-Noether number, $ \rho (g,r,d): = g - (r + 1)(g - d + r) = 0$. We prove that if $ r + 1 \ne g - d + r$, then for suitable families of curves $ (C/B)$, the monodromy of the family $ G_d^r(C/B) \to B$ is at least the alternating group. Our techniques are combinatorial, and similar to those used by Bercov and Proctor in their paper [BP].


References [Enhancements On Off] (What's this?)

  • [ACGH] E. Arbarello, M. Cornalba, P. Griffiths, and J. Harris, The geometry of algebraic curves, Springer-Verlag, New York, 1984.
  • [BP] Ronald D. Bercov and Robert A. Proctor, Solution of a combinatorially formulated monodromy problem of Eisenbud and Harris, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 2, 241–250. MR 911757
  • [EH] David Eisenbud and Joe Harris, Irreducibility and monodromy of some families of linear series, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 65–87. MR 892142

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DOI: https://doi.org/10.1090/S0002-9939-1991-1069686-X
Article copyright: © Copyright 1991 American Mathematical Society

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