Related papers: On the rational Enriques-Fano threefolds discovere…

We classify primitive Fano threefolds in positive characteristic whose Picard numbers are at least two. We also classify Fano theefolds of Picard rank two.

In order to find useful information to complete the classification of Enriques-Fano threefolds, we will computationally study the singularities of some known Enriques-Fano threefolds of genus 6, 7, 8, 9, 10, 13 and 17. We will also deduce…

We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.

We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.

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

A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We…

We prove that $\mathbb{Q}$-Fano threefolds of Fano index $\ge 8$ are rational.

We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of $\mathbb{R}$-rationality.

We shall prove that the threefold studied in the paper "Remarks on an Example of K. Ueno" by F. Campana is unirational. This gives an affirmative answer to a question posed in the paper above and also in the book by K. Ueno, "Classification…

We give a classification of Fano threefolds $X$ with canonical Gorenstein singularities such that $X$ possess a regular involution, which acts freely on some smooth surface in $|-K_X|$, and the linear system $|-K_X|$ gives a morphism which…

This paper is a sequel to [arXiv:2403.18389]. We investigate the rationality problem for $\mathbf{Q}$-Fano threefolds of Fano index $\ge 3$.

In this paper we study Fano threefolds with a torsion divisor (Fano--Enriques). Due to this torsion divisor, they can be described as quotients of Fano threefolds by a finite abelian group action. We start from lists of Fano threefolds by…

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface…

We classify smooth Fano threefolds with infinite automorphism groups.

We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.

Over an algebraically closed field of positive characteristic, we classify smooth Fano threefolds of Picard number one whose anti-canonical linear systems are not very ample. Furthermore, we also prove that an anti-canonically embedded Fano…

We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic.

The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.

We investigate the rationality problem for $\mathbf{Q}$-Fano threefolds of Fano index $\ge 2$.

We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.