On G-Fano threefolds

TL;DR

This paper investigates G-Fano threefolds with terminal singularities, establishing conditions under which they lack planes and providing bounds on their singular points, advancing understanding of their geometric structure.

Contribution

It introduces new conditions preventing planes in G-Fano threefolds and derives upper bounds on singular points for certain classes of these varieties.

Findings

G-Fano threefolds with certain assumptions do not contain planes

Upper bounds are established for the number of singular points

Results contribute to classification of Fano threefolds with terminal singularities

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.