On G-Fano threefolds

Abstract

We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of singular points of certain Fano threefolds with~terminal factorial singularities.

17 pages

Cited by in corpus (43)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• The rationality problem for conic bundles
• K-stability of Fano varieties: an algebro-geometric approach
• Codimension one holomorphic distributions on the projective three-space
• On terminal Fano 3-folds with 2-torus action
• On torus actions of higher complexity
• Singular Fano threefolds of genus 12
• Fano threefolds as equivariant compactifications of the vector group
• Subgroups of odd order in the real plane Cremona group
• Birational geometry of del Pezzo fibrations with terminal quotient singularities
• On deformations of toric Fano varieties
• On toric geometry and K-stability of Fano varieties
• On holomorphic distributions on Fano threefolds
• Lagrangian torus fibration models of Fano threefolds
• On smooth Fano fourfolds of Picard number two
• Projecting Fanos in the mirror
• Standard models of degree $1$ del Pezzo fibrations
• Burkhardt quartic, Barth sextic, and the icosahedron
• p-subgroups in the space Cremona group
• Integral points of bounded height on a log Fano threefold
• Polyvector fields for Fano 3-folds
• New examples of cylindrical Fano fourfolds
• Toric $G$-Fano Threefolds
• On Fano threefolds with ${\mathbb{C}}^{\ast }$-action
• An introduction to Geometric Manin's conjecture
• Derived categories of nodal del Pezzo threefolds
• 15-nodal quartic surfaces.I: quintic del Pezzo surfaces and congruences of lines in $\bbP^3$
• Uniformisation of higher-dimensional minimal varieties
• Obstructions to deforming curves on a prime Fano 3-fold
• Jordan constant for Cremona group of rank 3
• Finite groups of birational transformations
• Rationally connected threefolds with nef and bad anticanonical divisor
• Balanced line bundles on Fano varieties
• Four dimensional Fano quiver flag zero loci (with an appendix by T. Coates, E. Kalashnikov, and A. Kasprzyk)
• Fano-Mukai fourfolds of genus $10$ as compactifications of ${\mathbb{C}}^4$
• Rationality of Fano threefolds with terminal Gorenstein singularities, I
• A Weak Fano Threefold Arising as a Blowup of a Curve of Genus 5 and Degree 8 on ${\mathbb{P}}^3$
• On terminal Fano 3-folds with 2-torus action, part II
• On the existence of almost Fano threefolds with del Pezzo fibrations
• Nodal quintic del Pezzo threefolds and their derived categories
• Quartic double solids with icosahedral symmetry
• Simple isotropic decompositions of the curve sections of the known Enriques-Fano threefolds
• Conic bundle structures on Q-Fano threefolds