Related papers: On some Fano--Enriques threefolds
We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein…
We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.
We study the K-stability of singular Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system is base-point-free but not very ample.
We classify nonrational Fano threefolds $X$ with terminal Gorenstein singularities such that $\mathrm{\rk}\, \mathrm{\Pic}(X)=1$, $(-K_X)^3\ge 8$, and $\mathrm{\rk}\, \mathrm{\Cl}(X)\le 2$.
We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.
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 classify toric Fano threefolds having at worst terminal singularities such that a rank of a $G$-invariant part of a class group equals one, where $G$ is a group acting on the variety by automorphisms.
We consider Fano threefolds $X$ with canonical Gorenstein singularities. Under additional assumption that $X$ has at least one non-cDV point we prove a sharp bound of the degree: $-K_X^3\le 72$.
We classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.
We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.
We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.
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…
We consider Fano threefolds $V$ with canonical Gorenstein singularities. A sharp bound $-K_V^3\le 72$ of the degree is proved.
We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin's Conjecture for smooth Fano threefolds, including the classification of subvarieties with…
We prove that the linear system $|-1/3K_X| on a non-singular Fano fivefold $X$ of index 3 contains an irreducible divisor with only canonical singularities.
We classify Fano threefolds with only Gorenstein terminal singularities and Picard number greater than 1 satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action…
We classify smooth Fano threefolds with infinite automorphism groups.
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…
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…
For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties to toric Fano varieties with at most…