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On threefolds with low sectional genus

Published online by Cambridge University Press:  22 January 2016

Mauro Beltrametti  and
Marino Palleschi
Mauro Beltrametti
Affiliation:
1st. Matematico Via L. B. Alberti, U 16132 Genova, Italy
Marino Palleschi
Affiliation:
1st. Matematico Via L. B. Alberti, U 16132 Genova, Italy
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The general problem of rebuilding the threefolds X endowed with a given ample divisor H, possibly non-effective, is closely related to the study of the complete linear system |KX + H| adjoint to H. Many powerful results are known about |KX + H|, for instance when the linear system | H | contains a smooth surface or, more particularly, when H is very ample (e.g. see Sommese [S1] and [S2]). From this point of view we study some properties of |KX + H |, which turn out to be very useful in the description of the threefolds X polarized by an ample divisor H whose arithmetic virtual genus g(H) is sufficiently low.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 101 , March 1986 , pp. 27 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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