Related papers: G-Fano threefolds, I
In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.
This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3,Z), all convex polytopes in Z^3 which contain the origin as…
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 classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.
This is the unabridged web version of the paper that will be published on the American Journal of Mathematics. In this paper, we study the birational geometry of certain examples of mildly singular quartic 3-folds. A quartic 3-fold is an…
In this article, we determine all equivariant compactifications of the three-dimensional vector group $\mathbf{G}_a^3$ which are smooth Fano threefolds with Picard number greater or equal than two.
We classify all $\mathbb{Q}$-factorial Fano intrinsic quadrics of dimension three and Picard number one having at most canonical singularities.
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…
Abstract. In our previous paper arXiv:2210.16008, we show that any prime $\mathbb{Q}$-Fano 3-folds $X$ with only $1/2(1,1,1)$-singularities in certain 5 classes can be embedded as linear sections into bigger dimensional $\mathbb{Q}$-Fano…
We consider Fano threefolds $V$ with canonical Gorenstein singularities. A sharp bound $-K_V^3\le 72$ of the degree is proved.
We classified prime $\mathbb{Q}$-Fano $3$-folds $X$ with only $1/2(1,1,1)$-singularities and with $h^{0}(-K_{X})\geq 4$ a long time ago. The classification was undertaken by blowing up each $X$ at one $1/2(1,1,1)$-singularity and…
We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.
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.
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 construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetric matrices, and can be seen as higher-dimensional analogues…
We classify birationally rigid orbifold Fano 3-folds of index one defined by $5 \times 5$ Pfaffians. We give a sharp criterion for birational rigidity of these families based on the type of singularities that the varieties admit. Various…
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 all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds…
Let $\mathcal{X}$ be a smooth Fano threefold over the complex numbers of Picard rank $1$ with finite automorphism group. We give numerical restrictions on the order of the automorphism group $\mathrm{Aut}(\mathcal{X})$ provided the genus…
The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric $G$-varieties of rank 2 which are Fano. When $G$ is…