Related papers: Birationally solid Fano 3-fold hypersurfaces

We prove that all general smooth Fano threefolds of Picard rank $3$ and degree $14$ are K-stable, where the generality condition is stated explicitly.

In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…

We characterise smooth curves in a smooth cubic threefold whose blow-ups produce a weak-Fano threefold. These are curves $C$ of genus $g$ and degree $d$, such that (i) $2(d-5) \le g$ and $d\le 6$; (ii) $C$ does not admit a 3-secant line in…

Let $V_1$ be the Fano threefold given as a hypersurface of degree 6 in $P(1,1,1,2,3)$ (over a number field $K$). Then there exists a finite extension $K'/K$ such that the set of $K'$-rational points of $X$ is Zariski dense.

Let $X$ be a complex smooth Fano variety of dimension $n$. Assume that $X$ admits a birational contraction of an extremal ray. In this paper, we give a classification of such $X$ when the pseudoindex is equal to $\frac{\dim X}{2}$.

In this paper we address Fano manifolds with positive higher Chern characters. They are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional…

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

This paper proposes the use of $F$-split and globally $F$-regular conditions in the pursuit of BAB type results in positive characteristic. The main technical work comes in the form of a detailed study of threefold Mori fibre spaces over…

We provide a systematic method to classify all smooth weak Fano toric varieties of Picard rank $3$ in any dimension using Macaulay2, and describe the classification explicitly in dimensions $3$ and $4$. There are $28$ and $114$ isomorphism…

Let $(X,L)$ be a quasi-polarized canonical Calabi-Yau threefold. In this note, we show that $\vert mL\vert$ is basepoint free for $m\geq 4$. Moreover, if the morphism $\Phi_{\vert 4L\vert}$ is not birational onto its image and $h^0(X,L)\geq…

T.Kishimoto raised the problem to classify all compactifications of contractible affine 3-folds into smooth Fano 3-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this…

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.

Let X be a Q-factorial Gorenstein Fano variety. Suppose that the singularities of X are canonical and that the locus where they are non-terminal has dimension zero. Let D be a prime divisor of X. We show that rho_X - rho_D < 9 (where rho is…

For a complex connected semisimple linear algebraic group $G$ of adjoint type and of rank $n$, De Concini and Procesi constructed its wonderful compactification $\bar{G}$, which is a smooth Fano $G \times G$-variety of Picard number $n$…

We prove divisorial canonicity of Fano double hypersurfaces of general position.

Let \phi: \mathbb{P}^{r}\dashrightarrow Z be a birational transformation with a smooth connected base locus scheme, where Z\subseteq\mathbb{P}^{r+c} is a nondegenerate prime Fano manifold. We call \phi a quadro-quadric special briational…

It was shown that in robustly transitive, partially hyperbolic diffeomorphisms on three dimensional closed manifolds, the strong stable or unstable foliation is minimal. In this article, we prove ``almost all'' leaves of both stable and…

For any positive integer $k$ and any integer $n$ large enough, we construct a Fano variety $X$ with Picard number $k$ and dimension $n$ such that $((-K_X)^n)^{1/n}$ grows like $n^k/(\log n)^{k-1}$.

In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables…

We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of $\mathbb{P}^3$ at one point branched along an anti-canonical divisor.