Hyperelliptic and trigonal Fano threefolds

By Ivan Cheltsov, Constantin Shramov, V. Przyjalkowski. 2004

53 citations recorded by the source corpus.

We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singu- larities which are not intersections of quadrics. We also study rationality questions for most of these varieties.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ac85c611c393c67cfa4a14441c91d73328260016

How researchers see this paper

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In Algebra and Number Theory

1. T. Peternell
2. Yuri Prokhorov

In Geometry and Topology

1. Yuri Prokhorov
2. T. Peternell
3. C. Birkar
4. Stefan Kebekus
5. Henri Guenancia
6. D. Greb

Citations in the corpus

• Simple finite subgroups of the Cremona group of rank 3 (2009, methodology): “hat the linear system |−KX| determines a morphism ϕ: X → Pg+1 and ϕis not an embedding. Let Y = ϕ(X). Then ϕis a generically double cover and Y ⊂ Pg+1 is a subvariety of degree g− 1 [Isk80], [Isk77], [PCS05]. Note that the action of Gon Xinduces a nontrivial (hence faithful) action of Gon ϕ(X) since”
• Threefolds with big and nef anticanonical bundles I (2004, background): “The classification of hyperelliptic Fano threefolds is due to Iskovskikh in the smooth case ([I78]) and to Cheltsov, Shramov and Przyjalkowski for Gorenstein Fano threefolds with canonical singularities ([ CSP04 ]).”