Fano hypersurfaces in weighted projective 4-spaces

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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.

Original languageEnglish (US)
Pages (from-to)151-158
Number of pages8
JournalExperimental Mathematics
Issue number1
StatePublished - Jan 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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