TY - JOUR

T1 - Fano hypersurfaces in weighted projective 4-spaces

AU - Johnson, jennifer M.

AU - Kollar, janos

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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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U2 - 10.1080/10586458.2001.10504438

DO - 10.1080/10586458.2001.10504438

M3 - Article

AN - SCOPUS:0040970362

VL - 10

SP - 151

EP - 158

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

IS - 1

ER -