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A Threefold of General Type with q 1=q 2=p g =P 2=0

A Threefold of General Type with q 1=q 2=p g =P 2=0 One of the problems in classifying nonsingular threefolds of general type with p g =0 lies in finding the range of the bigenus P 2 (surfaces of general type with p g =0 have 2≤P 2≤10). Another problem involves finding the minimum integer m such that the m-canonical map Φ|mK| is birational for any threefold (m=5 in the case of surfaces). An example of a nonsingular threefold X of general type with q 1=q 2=0, p g =P 2=0,P 3=1 is presented. In addition, the m-canonical map of X is birational if and only if m≥14. The threefold is obtained as a nonsingular model of a degree ten hypersurface in P 4 C with the affine equation t 2=f 10(x,y,z). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

A Threefold of General Type with q 1=q 2=p g =P 2=0

Acta Applicandae Mathematicae , Volume 75 (3) – Oct 5, 2004

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1022336011727
Publisher site
See Article on Publisher Site

Abstract

One of the problems in classifying nonsingular threefolds of general type with p g =0 lies in finding the range of the bigenus P 2 (surfaces of general type with p g =0 have 2≤P 2≤10). Another problem involves finding the minimum integer m such that the m-canonical map Φ|mK| is birational for any threefold (m=5 in the case of surfaces). An example of a nonsingular threefold X of general type with q 1=q 2=0, p g =P 2=0,P 3=1 is presented. In addition, the m-canonical map of X is birational if and only if m≥14. The threefold is obtained as a nonsingular model of a degree ten hypersurface in P 4 C with the affine equation t 2=f 10(x,y,z).

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 5, 2004

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