×

zbMATH — the first resource for mathematics

Existence, decomposition, and limits of certain Weierstrass points. (English) Zbl 0606.14014
Here, using the general theory of their previous paper [ibid. 85, 337-371 (1986; Zbl 0598.14003)] and the main result of the immediately preceding paper [ibid. 87, 485-493 (1987; see the review 14008)], the authors analyze the limit of Weierstrass points on a family of smooth curves degenerating to a reducible curve C with \(Pic^ 0(C)\) compact. The authors prove the existence of subvarieties of \(M_ g\) of the expected codimension and formed by curves with s Weierstrass points of prescribed gap sequence if the sum of the weights of the prescribed gap sequences is \(\leq g/2\).
Reviewer: E.Ballico

MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
14H10 Families, moduli of curves (algebraic)
14M15 Grassmannians, Schubert varieties, flag manifolds
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Arbarello, E.: Weierstrass points and moduli of curves. Compos. Math.29, 325-342 (1974) · Zbl 0355.14013
[2] Buchweitz, R.-O.: On Zariski’s criterion for equisingularity and non-smoothable monomial curves. Preprint 1980
[3] Diaz, S.: Tangent spaces in moduli via deformations with applications to Weierstrass points. Duke J. Math.51, 905-922 (1984a) · Zbl 0581.14019 · doi:10.1215/S0012-7094-84-05140-8
[4] Diaz, S.: Moduli of curves with two exceptional Weierstrass points. J. Differ. Geom.20, 471-478 (1984b) · Zbl 0565.14011
[5] Diaz, S.: Exceptional Weierstrass points and the divisor on moduli space that they define. Thesis, Brown Univ. 1982. Mem. Am. Math. Soc.56, 327 (1985)
[6] Diaz, S.: Deformations of exceptional Weierstrass Points. Proc. Am. Math. Soc.96, 7-10 (1986) · Zbl 0595.14014 · doi:10.1090/S0002-9939-1986-0813798-8
[7] 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
[8] Eisenbud, D., Harris, J.: Limit linear series: Basic theory. Invent. math.85, 337-371 (1986) · Zbl 0598.14003 · doi:10.1007/BF01389094
[9] Eisenbud, D., Harris, J.: Recent progress in the study of Weierstrass points. Conf. Proceedings, Rome 1984. Lect. Notes Math. (to appear) · Zbl 0581.14020
[10] Eisenbud, D., Harris, J.: The monodromy of Weierstrass points (to appear) · Zbl 0632.14014
[11] Eisenbud, D., Harris, J.: When ramification points meet. Invent. math.87, 485-493 (1987) · Zbl 0606.14008 · doi:10.1007/BF01389239
[12] Griffiths, P.A., Harris, J.: Principles of Algebraic Geometry. John Wiley and Sons, New York, 1978 · Zbl 0408.14001
[13] Haure, M.: Recherches sur les points de Weierstrass d’une coube plane algèbrique. Ann. de l’Ecole Normale13, 115-150 (1896) · JFM 27.0468.02
[14] Hensel, K., Landsberg, G.: Theorie der algebraischen Funktionen einer Variablen. Repr. by Chelsea, New York, 1965 (1902)
[15] Hurwitz, A.: Über algebraischer Gebilde mit eindeutigen Transformationen in sich. Math. Ann.41, 403-442 (1893) · JFM 24.0380.02 · doi:10.1007/BF01443420
[16] Knebl, H.: Ebene algebraische Kurven vom Typp, q. Manuscr. Math.49, 165-175 (1984) · Zbl 0575.14022 · doi:10.1007/BF01168749
[17] Kuribayashi, A., Komiya, K.: On Weierstrass points of non-hyperelliptic compact Riemann surfaces of genus three. Hiroshima Math. J.7, 743-768 (1977) · Zbl 0398.30035
[18] Laufer, H.: On generalized Weierstrass points and rings with no radically principle prime ideals. In: Riemann surfaces and related topics, ed. Kra, I., Maskit, B. (eds.). Annals of Math. Studies, vol. 97. Princeton: Princeton U. Press, 1981 · Zbl 0517.14005
[19] Lax, R.: Weierstrass points on the universal curve. Math. Ann.216, 35-42 (1975) · Zbl 0299.32015 · doi:10.1007/BF02547970
[20] Lax, R.: Gap sequences and moduli in genus4. Math. Z.175, 67-75 (1980) · Zbl 0436.32016 · doi:10.1007/BF01161382
[21] Littlewood, D.E.: The theory of group characters, (second ed.). Oxford: Oxford University Press, 1950 · Zbl 0038.16504
[22] Lugert, E.: Weierstrasspunkte kompakter Riemann’scher Flächen vom Geschlecht 3. Thesis, Universität Erlangen-Nürnberg, 1981 · Zbl 0487.30033
[23] Pinkham, H.: Deformations of algebraic varieties. Astérisque20 (1974) · Zbl 0304.14006
[24] Rim, D.S., Vittulli, M.: Weierstrass points and monomial curves. J. Algebra 454-476 (1977) · Zbl 0412.14002
[25] Schreyer, F.O.: Syzygies of curves with special pencils. Thesis, Brandeis Univ. 1983. Math. Ann.275, 105-137 (1986) · Zbl 0578.14002 · doi:10.1007/BF01458587
[26] Szpiro, L.: Propriétés numeriques du Faisceaux dualisant relative. Astérisque 86, 44-78 (1981)
[27] Vermeulen, A.M.: Weierstrass points of weight two on curves of genus three. Thesis, Amsterdam University, 1983 · Zbl 0534.14010
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.