Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0872.14025
Esteves, E.
Wronski algebra systems on families of singular curves. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 29, No. 1, 107-134 (1996). ISSN 0012-9593

The main purpose of the article is to construct, and study, Wronski systems on a family $X/S$ of curves. When $X/S$ is a family consisting of complete intersection reduced curves, the author constructs a Wronski system consisting of locally free $\Cal O_X$-modules $Q^i$ that have natural functorial properties and that fit into exact sequences $$0\to \omega^{\otimes i} \to Q^i \to Q^{i-1} \to 0,$$ where $\omega$ is the dualizing sheaf of the family. The $Q^i$ are unique with the functorial properties. To show that Wronski systems exist is important because they give rise to Wronski determinants whose zero loci give the Weierstrass points of the family. For a single integral Gorenstein curve Weierstrass points have been defined and studied by Widland in his thesis [see also {\it R. F. Lax} and {\it C. Widland}, Pac. J. Math. 50, No. 1, 111-122 (1991; Zbl 0686.14033) and {\it A. Garcia} and {\it R. F. Lax}, Commun. Algebra 22, No. 12, 4841-4854 (1994; Zbl 0824.14033)], and Wronski systems have been constructed by {\it D. Laksov} and {\it A. Thorup} [Ark. Mat. 32, No. 2, 393-422 (1994; Zbl 0839.14020)]. The latter authors also got results for certain families as a consequence of their work on Wronskian systems on schemes of arbitrary dimension. {\it E. Esteves} has later used residues to compare his approach with other approaches for families of curves [see Bol. Soc. Bras. Mat., Nova Sér. 26, No. 2, 229-243 (1995; Zbl 0855.14003)]. The present article shows that the previous results, in a natural way, can be extended to families of curves, and that reduced curves can be allowed in the family, as long as the family consists of complete intersections. The construction holds in any characteristic.
[D.Laksov (Stockholm)]

MSC 2000:: *14H55 Riemann surfaces
14H20 Singularities, local rings
14H10 Families, algebraic moduli (curves)
14M10 Complete intersections

Keywords: Wronski systems; Weierstrass points; families of curves; complete intersections

Citations: Zbl 0725.14022; Zbl 0824.14033; Zbl 0839.14020; Zbl 0855.14003; Zbl 0686.14033

Cited in: Zbl 1063.14033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]