On images and inverse images of Weierstrass points†

Lax, R. F.

Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 125-128

Résumé

The classical theory of Weierstrass points on a compact Riemann surface is well-known (see, for example, [3]). Ogawa [6] has defined generalized Weierstrass points. Let Y denote a compact complex manifold of (complex) dimension n. Let E denote a holomorphic vector bundle on Y of rank q. Let Jk(E) (k = 0, 1, ...) denote the holomorphic vector bundle of k-jets of E [2, p. 112]. Put rk(E) = rank Jk(E) = q.(n + k)!/n!k!. Suppose that Γ(E), the vector space of global holomorphic sections of E, is of dimension γ(E)>0. Consider the trivial bundle Y × Γ(E) and the mapwhich at a point Q∈Y takes a section of E to its k-jet at Q. Put μ = min(γ(E),rk(E)).

Détail

DOI : 10.1017/S0017089500003505

Bibliographie

[1] 1.Altman, A. and Klciman, S., Introduction to Grothendieck duality theory, Lecture Notes in Mathematics No. 146 (Springer-Verlag, 1970). Google Scholar | DOI

[2] 2.Golubitsky, M. and Guillemin, V., Stable mappings and their singularities (Springer-Verlag, 1973). Google Scholar

[3] 3.Gunning, R. C., Lectures on Riemann surfaces (Princeton University Press, Princeton, N.J., 1966). Google Scholar

[4] 4.Hirzebruch, F., Topological methods in algebraic geometry, Third edition (Springer-Verlag, 1966). Google Scholar

[5] 5.Lax, R. F., Weierstrass points of products of Riemann surfaces, Pacific J. Math. 66 (1976), 191–194. Google Scholar | DOI

[6] 6.Ogawa, R. H., On the points of Weierstrass in dimension greater than one, Trans. Amer. Math. Soc. 184 (1973), 401–417. Google Scholar | DOI

[7] 7.Rauch, H. E. and Farkas, H. M., Theta functions with applications to Riemann surfaces (Williams and Wilkins, Baltimore, 1974). Google Scholar