Affordable Access

Correction to “Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one”

Authors
Publication Date
Disciplines
  • Law

Abstract

Correction to “Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one” COMPOSITIO MATHEMATICA ECKARTVIEHWEG Correction to “Canonical divisors and the additivity of theKodaira dimension formorphisms of relative dimension one” Compositio Mathematica, tome 35, no 3 (1977), p. 336-336. <http://www.numdam.org/item?id=CM_1977__35_3_336_0> © Foundation Compositio Mathematica, 1977, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http:// http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pé- nale. Toute copie ou impression de ce fichier doit contenir la pré- sente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 336 CORRECTION TO "CANONICAL DIVISORS AND THE ADDITIVITY OF THE KODAIRA DIMENSION FOR MORPHISMS OF RELATIVE DIMENSION ONE"* Eckart Viehweg COMPOSITIO MATHEMATICA, Vol. 35, Fasc. 3, 1977, pag. 336 Noordhoff International Publishing Printed in the Netherlands Trying to make the application of duality theory as easy as pos- sible, 1 made a silly mistake in Corollary 5.3, claiming, that the singularities of V’, W’ and Vs are Gorenstein. However (as the participants of the Conference on Algebraic Geometry in Avignon pointed out to me) it is only true, that they are Cohen-Macaulay and that some power of the canonical sheaves are invertible. This is easily shown for every quotient singularity and since 1Ts is a flat Gorenstein morphism, for V, too. You have to argue slightly differently to prove: Using the notation of 6.7 and the arguments used in 6.5, we get an isomorphism f*03C9v, ~ úJVs and hence a morphism f*03C9vs ~ 03C9v,. We can apply 6.1 iii) to hl, h, g and to the flat morphism 71’s’ Choose r EN, such that the r-th power of ever

There are no comments yet on this publication. Be the first to share your thoughts.