Related papers: Fano type surfaces with large cyclic automorphisms

Based on the former parts, we classify smooth Fano threefolds of positive characteristic.

We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete…

We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.

We overview some recent results on Fano varieties giving evidence of their rigid nature under small deformations.

This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.

The purpose of the present paper is to generalize Sakai's work on anticanonical models of rational surfaces to varieties of Fano type. We first prove a characterization of Fano type varieties using the singularities of anticanonical models.…

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

We give examples of Fano varieties $X$ with Picard number 1, which have terminal singularities and admit endomorphisms with degree larger than 1.

We classify Q-Fano threefolds of Fano index > 2 and big degree.

We prove birational superrigidity of Fano cyclic covers of index 1 over hypersurfaces in the projective space.

We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.

We give a classification of smooth Fano fourfolds such that the base scheme of the anticanonical system is a smooth surface. As a consequence we show that there are exactly 22 deformation families of such manifolds and they are all obtained…

We study the configurations of genus 2 curves on the Fano surfaces of cubic threefolds. We establish a link between some involutive automorphisms acting on such a surface S and genus 2 curves on S. We give a partial classification of the…

We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.

We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.

It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

We present the construction of Inoue surfaces of type $S^{(+)}/S^{(-)}$ in terms of data arising from real quadratic number fields. We then describe the automorphism group of such surfaces in terms of this data.

A cyclic $n$-gonal surface is a compact Riemann surface $X$ of genus $g\geq 2$ admitting a cyclic group of conformal automorphisms $C$ of order $n$ such that the quotient space $X/C$ has genus 0. In this paper, we provide an overview of…

We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.