×

zbMATH — the first resource for mathematics

Limit linear series: Basic theory. (English) Zbl 0598.14003
In this important paper the authors study the relation of linear series on a stable curve C with \(Pic^ 0(C)\) compact and the linear series on nearby smooth curves. In papers which will appear soon, they apply their theory to many important topics (Kodaira dimension of \(M_ g\), existence and monodromy of Weierstrass points). For another application, see the reviewer, Proc. Am. Math. Soc. 97, 217-218 (1986; Zbl 0591.14020).
Reviewer: E.Ballico

MSC:
14C20 Divisors, linear systems, invertible sheaves
14H10 Families, moduli of curves (algebraic)
14H15 Families, moduli of curves (analytic)
14D15 Formal methods and deformations in algebraic geometry
14H45 Special algebraic curves and curves of low genus
14H55 Riemann surfaces; Weierstrass points; gap sequences
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Arbarello, e., Cornalba, M., Griffiths, P., Harris, J.: Geometry of Algebraic Curves. Berlin-Heidelberg-New York-Tokyo: Springer 1984 · Zbl 0559.14017
[2] Beauville, A.: Prym varieties and the Schottky problem. Invent. Math.41, 149-196 (1977) · Zbl 0354.14013 · doi:10.1007/BF01418373
[3] Castelnuovo, G.: Numero delle involutione razionali giacenti sopra una curva di dato genere. Rend. R. Acad. Lincei, Ser 4,5 (1889) · JFM 21.0668.01
[4] Diaz, S.: Exceptional Weierstrass points and the divisor on moduli space that they define. Thesis, Brown University 1982
[5] Eisenbud, D., Harris, J.: Divisors on general curves and cuspidal rational curves. Invent. Math.74, 371-418 (1983) · Zbl 0527.14022 · doi:10.1007/BF01394242
[6] Eisenbud, D., Harris, J.: On the Brill-Noether Theorem. In:Algebraic Geometry?Open Problems. Proceedings, Ravello 1982, Ed. C. Ciliberto, F. Ghione, and F. Orecchia, Lect. Notes Math.997, 131-137 (1983)
[7] Eisenbud, D., Harris, J.: A simpler proof of the Gieseker-Petri Theorem on special divisors. Invent. Math.74, 269-280 (1983) · Zbl 0533.14012 · doi:10.1007/BF01394316
[8] Eisenbud, D., Harris, J.: Existence and degeneration of Weierstrass points of low weight. Invent. Math. (to appear) · Zbl 0606.14014
[9] Eisenbud, D., Harris, J.: The monodromy of Weierstrass points. Invent. Math. (to appear) · Zbl 0632.14014
[10] Eisenbud, D., Harris, J.: The irreducibility of some families of linear series. (Preprint 1984) · Zbl 0533.14013
[11] Eisenbud, D., Harris, J.: On the Kodaira dimension of the moduli space of curves. Invent. Math. (to appear) · Zbl 0631.14023
[12] Eisenbud, D., Harris, J.: When ramification points meet. (Preprint) · Zbl 0606.14008
[13] Fulton, W., Lazarsfeld, R.: On the connectedness of degeneracy loci and special divisors. Acta Math.146, 271-283 (1981) · Zbl 0469.14018 · doi:10.1007/BF02392466
[14] Gieseker, D.: Stable curves and special divisors. Invent. Math.66, 251-275 (1982) · Zbl 0522.14015 · doi:10.1007/BF01389394
[15] Griffiths, P., Harris, J.: On the variety of linear systems on a general algebraic curve. Duke Math. J.47, 233-272 (1980) · Zbl 0446.14011 · doi:10.1215/S0012-7094-80-04717-1
[16] Harris, J.: The Kodaira dimension of the moduli space of curves II: The even genus case. Invent. Math.75, 437-466 (1984) · Zbl 0542.14014 · doi:10.1007/BF01388638
[17] Harris, J., Mumford, D.: On the Kodaira dimension of the moduli space of curves. Invent. Math.67, 23-86 (1982) · Zbl 0506.14016 · doi:10.1007/BF01393371
[18] Kempf, G.: Schubert methods with an application to algebraic curves. Publ. Math. Centrum. University of Amsterdam 1971 · Zbl 0223.14018
[19] Kempf, G., Knudson, F., Mumford, D., Saint-Donat, B.: Toroidal Embeddings I. Lect. Notes Math.339, (1973) · Zbl 0271.14017
[20] Kleiman, S.L., Laksov, D.: Another proof of the existence of special divisors. Acta Math.132, 163-176 (1974) · Zbl 0286.14005 · doi:10.1007/BF02392112
[21] Knudsen, F., Mumford, D.: The projectivity of the moduli space of stable curves I: preliminaries on ?det? and ?Div?. Math. Scand.39, 19-55 (1976) · Zbl 0343.14008
[22] Knudsen, F., The projectivity of the moduli space of curves II: The stacksM g, n . Math. Scand.52, 161-199 (1983) · Zbl 0544.14020
[23] Knudsen, F.: The projectivity of the moduli space of curves III: The line bundles onM g,n and a proof of the projectivity of \(\bar M_{g,n} \) in characteristic 0. · Zbl 0544.14021
[24] Mumford, d.: Stability of projective varieties. Enseign. Math.23, 39-110 (1977) · Zbl 0363.14003
[25] Sernesi, E.: On the existence of certain families of curves. Invent. Math.75, 25-57 (1984) · Zbl 0541.14024 · doi:10.1007/BF01403088
[26] Serre, J.-P.: Groupes Algébriques et Corps de Classes. Actualités scientifiques et industrielles 1264. Hermann, Paris 1959
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.