G-Fano threefolds, I

Abstract

We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2, and satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action of some group $G$. In particular, we find a lot of examples of Fano 3-folds with "many" symmetries.

arXiv comment36 pages, LaTeX2e, a few typos are corrected

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• G-Fano threefolds, I
• Bounds for the orders of the finite subgroups of G(k)
• p-elementary subgroups of the Cremona group of rank 3
• Five embeddings of one simple group
• On the Picard number of almost Fano threefolds with pseudo-index >1

Cited by in corpus (14)

• On G-Fano threefolds
• G-Fano threefolds, I
• Which quartic double solids are rational?
• Singular Fano threefolds of genus 12
• 2-elementary subgroups of the space Cremona group
• On the number of singular points of factorial terminal Fano threefolds
• Birational geometry of del Pezzo fibrations with terminal quotient singularities
• Coble fourfold, $S_6$-invariant quartic threefolds, and Wiman-Edge sextics
• Burkhardt quartic, Barth sextic, and the icosahedron
• Kaehler-Einstein Fano threefolds of degree 22
• Toric $G$-Fano Threefolds
• Rationality of Fano threefolds with terminal Gorenstein singularities, I
• Fano-Mathieu correspondence
• Connected algebraic groups acting on Fano fibrations over ${\mathbb{P}}^1$