Related papers: The classification of smooth toric weakened Fano 3…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
In this notes we classify toric Fano 4-folds having positive second Chern Character.
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 provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.
In this note we collect some results on the deformation theory of toric Fano varieties.
We find all K-stable smooth Fano threefolds in the family No. 2.22.
The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such…
We find at least 527 new four-dimensional Fano manifolds, each of which is a complete intersection in a smooth toric Fano manifold.
This article constructs a smooth weak Fano threefold of Picard number two with small anti-canonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano was…
We prove the existence of asymptotically cylindrical (ACyl) Calabi-Yau 3-folds starting with (almost) any deformation family of smooth weak Fano 3-folds. This allow us to exhibit hundreds of thousands of new ACyl Calabi-Yau 3-folds;…
In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror…
We study toric G-solid Fano threefolds that have at most terminal singularities, where G is an algebraic subgroup of the normalizer of a maximal torus in their automorphism groups.
We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.
Kawakami and the author showed that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. That was a new way to analyze which varieties have nontrivial endomorphisms. In…
We construct families of non-toric $\mathbb{Q}$-factorial terminal Fano ($\mathbb{Q}$-Fano) threefolds of codimension $\geq 20$ corresponding to 54 mutation classes of rigid maximally mutable Laurent polynomials. From the point of view of…
This article gives an overview of toric Fano and toric weak Fano varieties associated to graphs and building sets. We also study some properties of such toric Fano varieties and discuss related topics.
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 present a combinatorial criterion on reflexive polytopes of dimension 3 which gives a local-to-global obstruction for the smoothability of the corresponding Fano toric threefolds. As a result, we show examples of singular Gorenstein Fano…
We produce a list of 64 families of Fano fourfolds of K3 type, extracted from our database of at least 634 Fano fourfolds constructed as zero loci of general global sections of completely reducible homogeneous vector bundles on products of…
We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.