Related papers: Canonical toric Fano threefolds
In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds which admit toric degenerations to toric Fano varieties with singularities…
We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for…
In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth…
We give a characterization of Gorenstein toric Fano varieties of dimension $n$ with index $n$ among toric varieties. As an application, we give a strong version of Fujita's freeness conjecture and also give a simple proof of Fujita's very…
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 characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We work out the case of complete intersections in toric varieties defined by non-degenerate…
This paper classifies toric Fano 3-folds with singular locus { 1/k(1,1,1) } for any positive integer k, building on the work of Batyrev and Watanabe-Watanabe. This is achieved by completing an equivalent problem in the language of Fano…
We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.
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 classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Pl\"ucker polarization) and study the fixed loci.
We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to…
We study singular Fano threefolds of type $V_{22}$.
We give a complete classification of smooth, complex projective Fano 4-folds of Picard number 3 having a prime divisor of Picard number 1. They form 28 distinct families, and we compute the main numerical invariants, study the base locus of…
We investigate the variation of log canonical thresholds in (graded) linear systems. For toric log Fano varieties, we give a sharp lower bound for log canonical thresholds of the anticanonical members in terms of the global minimal log…
We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of…
We construct a deformation family for each of the 34 Hilbert series of index 2 Fano 3-folds. In 18 cases we construct two different families, distinguished by the topology of their general members.
In this paper, we study the explicit geometry of threefolds, in particular, Fano varieties. We find an explicitly computable positive integer $N$, such that all but a bounded family of Fano threefolds have $N$-complements. This result has…
We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$.
We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.