Four-dimensional projective orbifold hypersurfaces
Brown, Gavin and Kasprzyk, Alexander M. (2015) Four-dimensional projective orbifold hypersurfaces. Experimental Mathematics, 25 (2). pp. 176-193. ISSN 1944-950X
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.
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