Higher dimensional polarized varieties with non-integral nefvalue

Higher dimensional polarized varieties with non-integral nefvalue Abstract. Let X be an n-dimensional normal projective variety with terminal, Gorenstein, Qfactorial singularities. Let L be an ample line bundle on X . Let t be the nefvalue of ðX ; LÞ. Then we classify ðX ; LÞ, describing the structure of the nefvalue morphism of ðX ; LÞ, when t satisfies n À k < t < n À k þ 1 and n d 2k À 3, k d 4. In the smooth case, we discuss the case n ¼ 2k À 4, k d 5, as well. Key words. Complex polarized n-fold, ample line bundle, nefvalue, nefvalue morphism, Gorenstein, terminal, Q-factorial singularities, adjunction theory, special varieties. 2000 Mathematics Subject Classification. Primary 14N30, 14J40; Secondary 14J45, 14C20 Introduction Let X be an n-dimensional projective variety with terminal, Gorenstein, Q-factorial singularities and let L be an ample line bundle on X . If the canonical bundle KX is not nef, the Kawamata rationality theorem and the Kawamata­Shokurov basepoint free theorem imply that there is a fraction t ¼ u=v, with u, v positive coprime integers, and a morphism f : X ! W with connected fibers onto a normal projective variety W such that vKX þ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Higher dimensional polarized varieties with non-integral nefvalue

Advances in Geometry, Volume 3 (3) – Aug 19, 2003

Loading next page...
 
/lp/de-gruyter/higher-dimensional-polarized-varieties-with-non-integral-nefvalue-hYXeiqQVOl
Publisher
de Gruyter
Copyright
Copyright © 2003 by the
ISSN
1615-715X
DOI
10.1515/advg.2003.017
Publisher site
See Article on Publisher Site

Abstract

Abstract. Let X be an n-dimensional normal projective variety with terminal, Gorenstein, Qfactorial singularities. Let L be an ample line bundle on X . Let t be the nefvalue of ðX ; LÞ. Then we classify ðX ; LÞ, describing the structure of the nefvalue morphism of ðX ; LÞ, when t satisfies n À k < t < n À k þ 1 and n d 2k À 3, k d 4. In the smooth case, we discuss the case n ¼ 2k À 4, k d 5, as well. Key words. Complex polarized n-fold, ample line bundle, nefvalue, nefvalue morphism, Gorenstein, terminal, Q-factorial singularities, adjunction theory, special varieties. 2000 Mathematics Subject Classification. Primary 14N30, 14J40; Secondary 14J45, 14C20 Introduction Let X be an n-dimensional projective variety with terminal, Gorenstein, Q-factorial singularities and let L be an ample line bundle on X . If the canonical bundle KX is not nef, the Kawamata rationality theorem and the Kawamata­Shokurov basepoint free theorem imply that there is a fraction t ¼ u=v, with u, v positive coprime integers, and a morphism f : X ! W with connected fibers onto a normal projective variety W such that vKX þ

Journal

Advances in Geometryde Gruyter

Published: Aug 19, 2003

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off