Anticanonical system of Fano fivefolds

Abstract

We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover,if a general element of the anticanonical system is reduced, then it has canonical singularities. We also prove nonvanishing of anticanonical system in the case of log canonical Gorenstein singularities.

arXiv comment6 pages, final version, to appear in Mathematische Nachrichten, added theorem concerning nonvanishing in case of log canonical Gorenstein Fano fivefold

References in corpus (3)

• Existence of minimal models for varieties of log general type
• Existence of good divisors on Mukai varieties
• Second Chern class of Fano manifolds and anti-canonical geometry

Cited by in corpus (5)

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• Laurent polynomials in Mirror Symmetry: why and how?
• Adjunction for varieties with a ${\mathbb{C}}^{\ast }$ action
• Stability of syzygy bundles on varieties of Picard number one
• On Subvarieties of Degenerations of Fano Varieties