Hyperelliptic and trigonal Fano threefolds

2004/06/30 by Ivan Cheltsov, Constantin Shramov, Victor Przyjalkowski
Mathematics · #math.AG #msc:14J30 #msc:12J17 #msc:14E08 #msc:14E05

paper · pdf

published as Izv. Math., 2005, 69 (2), 365-421 · 57 pages. Final version; more detailed version is the previous one

arxiv created 2005/06/13 · arxiv updated 2009/12/01

Abstract

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 singularities which are not intersections of quadrics. We also study the rationality questions for most of these varieties.

Related

• Rationality of Fano threefolds with terminal Gorenstein singularities, I
• Gorenstein Fano threefolds with base points in the anticanonical system
• Gorenstein Fano threefolds with base points in the anticanonical system
• Fano threefolds with canonical Gorenstein singularities and big degree
• Rationality of Fano threefolds with terminal Gorenstein singularities,\n II