Impacto
Downloads
Downloads per month over past year
Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P. (2003) Triple canonical covers of varieties of minimal degree. In A Tribute to C.S. Seshadri: A Collection of Articles on Geometry and Representation Theory. Trends in mathematics . Birkhauser Verlag Ag, Boston, pp. 241270. ISBN 3764304448

PDF
249kB 
Official URL: http://arxiv.org/pdf/math/0205010.pdf
URL  URL Type 

http://arxiv.org  Organisation 
Abstract
In this article we study pluriregular varieties X of general type with basepointfree canonical bundle whose canonical morphism has degree 3 and maps X onto a variety of minimal degree Y. We carry out our study from two different perspectives. First we study in Section 2 and Section 3 the canonical ring of X describing completely the degrees of its minimal generators. We apply this to the study of the projective normality of the images of the pluricanonical morphisms of X. Our study of the canonical ring of X also shows that, if the dimension of X is greater than or equal to 3, there does not exist a converse to a theorem of M. Green that bounds the degree of the generators of the canonical ring of X. This is in sharp contrast with the situation in dimension 2 where such converse exists, as proved by the authors in a previous work. Second, we study in Section 4, the structure of the canonical morphism of X. We use this to show among other things the nonexistence of some a priori plausible examples of triple canonical covers of varieties of minimal degree. We also characterize the targets of flat canonical covers of varieties of minimal degree. Some of the results of Section 4 are more general and apply to varieties X which are not necessarily regular, and to targets Y that are scrolls which are not of minimal degree.
Item Type:  Book Section 

Uncontrolled Keywords:  Canonical bundle; Canonical ring 
Subjects:  Sciences > Mathematics > Algebraic geometry 
ID Code:  15429 
Deposited On:  30 May 2012 08:58 
Last Modified:  22 Aug 2018 09:19 
Origin of downloads
Repository Staff Only: item control page