Triple Canonical Covers of Varieties of Minimal Degree View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2003

AUTHORS

Francisco Javier Gallego , Bangere P. Purnaprajna

ABSTRACT

In this article we study pluriregular varieties X of general type with base-point-free 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 non-existence 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. More... »

PAGES

241-270

References to SciGraph publications

  • 1976-06. Algebraic surfaces of general type with smallc12. II in INVENTIONES MATHEMATICAE
  • 1978-10. Algebraic surfaces of general type with smallc12. III in INVENTIONES MATHEMATICAE
  • 1978-06. Algebraic surfaces of general type with smallc12. IV in INVENTIONES MATHEMATICAE
  • 1991-03. Algebraic surfaces of general type withc12=3pg−6 in MATHEMATISCHE ANNALEN
  • Book

    TITLE

    A Tribute to C. S. Seshadri

    ISBN

    978-81-85931-39-5
    978-93-86279-11-8

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-93-86279-11-8_17

    DOI

    http://dx.doi.org/10.1007/978-93-86279-11-8_17

    DIMENSIONS

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