Four-dimensional projective orbifold hypersurfaces

Abstract

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi-Yau, and Fano fourfolds. We also consider other classes of hypersurfaces, including Fano hypersurfaces of index greater than 1 in dimensions 3 and 4.

25 pages

Cited by in corpus (10)

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• A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume
• Varieties of general type with doubly exponential asymptotics
• On minimal 4-folds of general type with $p_g\ge 2$
• On K-stability of Fano weighted hypersurfaces
• On smooth Calabi-Yau threefolds of Picard number two