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2001 Fano Hypersurfaces in Weighted Projective 4-Spaces
Jennifer M. Johnson, János Kollár
Experiment. Math. 10(1): 151-158 (2001).

Abstract

We determine the full list of anticanonically embedded quasismooth Fano hypersurfaces in weighted projective 4-spaces. There are 48 infinite series and 4442 sporadic examples. In particular, the Reid-Fletcher list of 95 types of anticanonically embedded quasismooth terminal Fano threefolds in weighted projective 4-spaces is complete. We also prove that many of these Fano hypersurfaces admit a Kähler-Einstein metric, and study the nonexistence of tigers on these Fano 3-folds. Finally, we prove that there are only finitely many families of quasismooth Calabi-Yau hypersurfaces in weighted projective spaces of any given dimension. This implies finiteness for various families of general type hypersurfaces.

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Jennifer M. Johnson. János Kollár. "Fano Hypersurfaces in Weighted Projective 4-Spaces." Experiment. Math. 10 (1) 151 - 158, 2001.

Information

Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 0972.14034
MathSciNet: MR1 822 861

Subjects:
Primary: 14Jxx

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 1 • 2001
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