Related papers: On Fano threefolds with canonical Gorenstein singu…

We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.

We consider Fano threefolds $V$ with canonical Gorenstein singularities. A sharp bound $-K_V^3\le 72$ of the degree is proved.

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: $-K_X^3\le 72$.

An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688…

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

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

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

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 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 classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.

For Fano varieties of various singularities such as canonical and terminal, we construct examples with large Fano index. By low-dimensional evidence, we conjecture that our examples have the largest Fano index for all dimensions.

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

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 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…

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 study three-dimensional Fano varieties with $\mathbb{C}^*$-action. Complementing recent results [13], we give classification results in the canonical case, where the maximal orbit quotient is $\mathbb{P}_2$ having a line arrangement of…

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…

We classify the cones of curves of Fano varieties of dimension greater or equal than five and (pseudo)index dim X -3, describing the number and type of their extremal rays.

We give a self-contained and simplified proof of Mukai's classification of prime Fano threefolds of index 1 and genus $g \ge 6$ with at most Gorenstein factorial terminal singularities, and of its extension to higher-dimension.