Related papers: Horospherical 2-Fano varieties
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 determine the stability/instability of the tangent bundles of the Fano varieties in a certain class of two orbit varieties, which are classified by Pasquier in 2009. As a consequence, we show that some of these varieties admit unstable…
We give a complete answer to the question of (semi)stability of tangent bundle of any nonsingular projective complex toric variety with Picard number 2 by using combinatorial crietrion of (semi)stability of an equivariant sheaf. We also…
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to…
Let $X$ be a complex smooth Fano variety of dimension $n$. In this paper, we give a classification of such $X$ when the pseudoindex is equal to $\dfrac{\dim X+1}{2}$ and the Picard number greater than one.
In this paper we study mildly singular del Pezzo foliations on complex projective manifolds with Picard number one
We show that for a weak $\mathbb{Q}$-Fano threefold $X$ ($\mathbb{Q}$-factorial with terminal singularities and $-K_X$ is nef and big) of Picard rank $\rho(X)\leq 2$, either $-K_X^3\leq 64$ or $-K_X^3=72$ and…
We present geometric realizations of horospherical two-orbit varieties, by showing that their blow-up along the unique closed-invariant orbit is the zero locus of a general section of a homogeneous vector bundle over some auxiliary variety.…
We obtain the exhaustive list of 337 faithful spherical actions of rank two or less on locally factorial Fano manifolds of dimension four or less. As a preliminary step, we determine the explicit list of spherical homogeneous spaces of…
Let X be a complex, Gorenstein, Q-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the…
A Fano variety of Picard number $1$ is said to be \textit{birationally solid} if it is not birational to a Mori fiber space over a positive dimensional base. In this paper we complete the classification of quasi-smooth birationally solid…
In this notes we classify toric Fano 4-folds having positive second Chern Character.
Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds…
Let X be a Fano manifold of pseudoindex i_X whose Picard number is at least two and let R be an extremal ray of X with exceptional locus Exc(R). We prove an inequality which bounds the length of R in terms of i_X and of the dimension of…
We prove a more general and precise version of the Noether-Fano inequalities for birational maps between Mori fiber spaces. This is applied to give descriptions of global canonical thresholds on Fano varieties of Picard number one.
We classify Q-Fano threefolds of Fano index > 2 and big degree.
We construct a family of examples of Legendrian subvarieties in some projective spaces. Although most of them are singular, a new example of smooth Legendrian variety in dimension 8 is in this family. The 8-fold has interesting properties:…
We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the…
Property $\mathcal{O}$ for an arbitrary complex, Fano manifold $X$, is a statement about the eigenvalues of the linear operator obtained from the quantum multiplication of the anticanonical class of $X$. Conjecture $\mathcal{O}$ is a…
We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups…