Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Multiples of Weierstrass points as special divisors


Author: R. F. Lax
Journal: Proc. Amer. Math. Soc. 82 (1981), 95-98
MSC: Primary 32G15; Secondary 14H15
DOI: https://doi.org/10.1090/S0002-9939-1981-0603608-1
MathSciNet review: 603608
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Complex spacss $ \mathcal{W}_n^r$ of Weierstrass points are isomorphic to the intersection, on the $ n$th symmetric product of the universal curve over the Teichmüller space, of complex spaces $ \mathcal{G}_n^r$ of special divisors with the diagonal $ {\Delta _n}$ consisting of divisors which are multiples of a point. The tangent space at a point of this intersection is described and it is shown that $ \mathcal{G}_n^1 - \mathcal{G}_n^2$ and $ {\Delta _n}$ intersect transversally.


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

  • [1] E. Arbarello and M. Cornalba, Su una congettura di Petri, Comment Math. Helv. (to appear). MR 615613 (82k:14029)
  • [2] R. C. Gunning, Lectures on Riemann surfaces: Jacobi varieties, Princeton Univ. Press, Princeton, N. J., 1972. MR 0357407 (50:9875)
  • [3] R. F. Lax, On the dimension of varieties of special divisors, Trans. Amer. Math. Soc. 203 (1975), 141-159. MR 0360602 (50:13049)
  • [4] -, Weierstrass points of the universal curve, Math. Ann. 216 (1975), 35-42. MR 0384809 (52:5681)
  • [5] -, Gap sequences and moduli in genus 4, Math. Z. 175 (1980), 67-75. MR 595632 (82a:32030)
  • [6] D. Mumford, Introduction to algebraic geometry (preliminary version of first 3 chapters), Harvard notes.
  • [7] M. Namba, Families of meromorphic functions on compact Riemann surfaces, Lecture Notes in Math., vol. 767, Springer-Verlag, Berlin, 1979. MR 555241 (82i:32046)
  • [8] C. Patt, Variations of Teichmüller and Torelli surfaces, J. Analyse Math. 11 (1963), 221-247. MR 0160894 (28:4103)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32G15, 14H15

Retrieve articles in all journals with MSC: 32G15, 14H15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603608-1
Keywords: Complex space, Weierstrass point, special divisor, Teichmüller space, universal curve
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society