Projective manifolds with small pluridegrees

Authors:
Mauro C. Beltrametti and Andrew J. Sommese

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3045-3064

MSC (1991):
Primary 14J40; Secondary 14M99, 14C20

DOI:
https://doi.org/10.1090/S0002-9947-99-02429-0

Published electronically:
May 21, 1999

MathSciNet review:
1641087

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Abstract: Let be a very ample line bundle on a connected complex projective manifold of dimension . Except for a short list of degenerate pairs , and there exists a morphism expressing as the blowup of a projective manifold at a finite set , with nef and big for the ample line bundle . The projective geometry of is largely controlled by the pluridegrees for , of . For example, , where is the genus of a curve section of , and is equal to the self-intersection of the canonical divisor of the minimal model of a surface section of . In this article, a detailed analysis is made of the pluridegrees of . The restrictions found are used to give a new lower bound for the dimension of the space of sections of . The inequalities for the pluridegrees, that are presented in this article, will be used in a sequel to study the sheet number of the morphism associated to .

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Additional Information

**Mauro C. Beltrametti**

Affiliation:
Dipartimento di Matematica, Università Degli Studi di Genova, Via Dodecaneso 35, I-16146 Genova, Italy

Email:
beltrame@dima.unige.it

**Andrew J. Sommese**

Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Email:
sommese@nd.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02429-0

Keywords:
Smooth complex polarized $n$-fold,
very ample line bundle,
adjunction theory,
log-general type,
pluridegrees.

Received by editor(s):
February 8, 1998

Published electronically:
May 21, 1999

Article copyright:
© Copyright 2000
American Mathematical Society