On the moduli spaces of Gorenstein curves with symmetric Weierstrass semigroups.

  title={On the moduli spaces of Gorenstein curves with symmetric Weierstrass semigroups.},
  author={Koichi Y. Takase and Karl-Otto St{\"o}hr},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={189 - 214}
There are two powerful tools, both based on deformation theory, to study the smooth projective pointed curves with a prescribed Weierstrass gap sequence f^ * f 2 , . . . , t. On the one band, Pinkham [Pi] constructs their moduli space by deforming irreducible singular affine curves, and on the other band Eisenbud and Harris [EH], by deforming reducible curves, obtain among many other results the existence of smooth curves whenever the 
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© Société mathématique de France, 1974, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les
(see ?1.1 for Der). We define functors Ti(B/A, M) and Ti(B/A, M) i=0, 1, 2 (for any B-module M) such that TO(B/A, M) = QB/A 0B M and TO(B/A, M) = DerA(B, M), and the Ti (resp. Ti) fit into nine term
Algebraic Geometry
Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)
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Die Wertehalbgruppe eines lokalen Rings der Dimension 1
Ist R eine multiplikativ abgeschlossene Teilmenge eines diskreten Bewertungsrings V mit 1∈R,so bilden die Werte der Elemente von R eine Unterhalbgruppe H der Halbgruppe der naturlichen Zahlen N mit