Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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AMPLE LINE BUNDLES ON TORIC FIBERED 3-FOLDS

Authors

  • Shoetsu Ogata

Keywords:

toric varieties, lattice polytopes

DOI:

https://doi.org/10.17654/0972087123005

Abstract

Let X be a projective nonsingular toric 3-fold with a surjective torus equivariant morphism onto the projective line or a nonsingular toric surface not isomorphic to the projective plane. Then we prove that an ample line bundle on X is always normally generated.

Received: November 11, 2022 
Accepted: December 26, 2022 

References

W. Bruns and J. Gubeladze, Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Springer, Dordrecht, Heidelberg, London, New York, 2009.

G. Ewald and U. Wessels, On the ampleness of line bundles in complete projective toric varieties, Results in Mathematics 19 (1991), 275-278.

W. Fulton, Introduction to toric varieties, Ann. of Math. Studies No. 131, Princeton Univ. Press, 1993.

D. Mumford, Varieties Defined by Quadric Equations, Questions on Algebraic Varieties, Corso CIME, 1969, pp. 29-100.

K. Nakagawa, Generators for the Ideal of a Projectively Embedded Toric Varieties, Thesis Tohoku University, 1994.

T. Oda, Convex Bodies and Algebraic Geometry, Ergebnisse der Math. 15, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.

S. Ogata, Projective normality of toric 3-folds with non-big adjoint hyperplane sections, Tohoku Math. J. 64 (2012), 125-140.

S. Ogata, Very ample but not normal lattice polytopes, Beitr. Zur Alg. Geom. 54 (2013), 291-302. Erratum to very ample but not normal lattice polytopes, Beitr. Zur Alg. Geom. 54 (2013), 769-770.

Published

2023-02-06

Issue

Section

Articles

How to Cite

AMPLE LINE BUNDLES ON TORIC FIBERED 3-FOLDS. (2023). Far East Journal of Mathematical Sciences (FJMS), 140(1), 71-87. https://doi.org/10.17654/0972087123005