Related papers: A remark on Fano threefolds with canonical Gorenst…

We prove that for $n \leq 4$ and $p > 5$, quasi--Gorenstein $F$--pure and $\mathbb{Q}_p$--rational $n$--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is…

We show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on Q-Fano threefolds, Gorenstein log del Pezzo surfaces and P^1. Similar results are obtained…

We study degree of irrationality of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces that have terminal singularities.

We study rationality properties of real singular cubic threefolds.

We obtain a sufficient condition for a Fano threefold with terminal singularities to have a conic bundle structure.

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

Let $M$ be a smooth Fano threefold such that a canonical extension of the tangent bundle is an affine manifold. We show that $M$ is rational homogeneous.

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano threefold over a finite field has a rational…

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 prove a structure theorem for non-isomorphic endomorphisms of weak Q-Fano threefolds, or more generally for threefolds with big anti-canonical divisor. Also provided is a criterion for a fibred rationally connected threefold to be…

We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.

We prove that very general non-rational Fano threefolds which are not birational to cubic threefolds are not stably rational.

In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.

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

We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…

We obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.

We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover,if a general element of the anticanonical system is reduced, then it has canonical singularities. We also prove…

In this article, we study how the rationality of a Fano threefold is reflected in its standard mirror Landau-Ginzburg model and its deformations. The main result is that a Fano threefold is rational if and only if the monodromy around every…

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…