Related papers: Unobstructedness of deformations of weak Fano mani…
In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.
We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the…
We study Fano manifolds of pseudoindex greater than one and dimension greater than five, which are blow-ups of smooth varieties along smooth centers of dimension equal to the pseudoindex of the manifold. We obtain a classification of the…
We construct a curvature varifold that does not admit a decomposition whose components are curvature varifolds.
We construct examples of Fano manifolds, which are defined over a field of positive characteristic, but not over $\com$.
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…
Let $X$ be a Fano manifold which is the zero scheme of a general global section $s$ in an irreducible homogenous vector bundle over a Grassmannian. We prove that the restriction of the Pl\"ucker embedding embeds $X$ projectively normal, and…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.
We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.
We generalize the Tian-Todorov Theorem in the case of Calabi-Yau varieties equipped with a line bundle.
In this short note we show the unboundedness of the dimension of the K-moduli space of $n$-dimensional Fano varieties, and that the dimension of the stack can also be unbounded while, simultaneously, the dimension of the corresponding…
As a special case of a conjecture by Schwede and Smith, we prove that a smooth complex projective threefold with nef anti-canonical divisor is weak Fano if it is of globally $F$-regular type.
We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of N\'eron-Severi spaces, nef cones, effective cones, movable cones, and…
We prove that the variety of complete flags for any semisimple algebraic group is rigid in any smooth family of Fano manifolds.
We prove the existence of Fano ladders on weak log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.
This paper generalizes the first author's preceding works concerning admissible functions on certain Fano manifolds. Here, we study a larger class of functions which can be less symmetric than the ones studied before. When the sup of these…
This article treats smooth weak Fano 3-folds having an extremal ray of type D. Smooth weak Fano 3-folds with an extremal ray of type D except of degree 6 are classified into 47 deformation types.
Fano varieties are subvarieties of the Grassmannian whose points parametrize linear subspaces contained in a given projective variety. These expository notes give an account of results on Fano varieties of complete intersections, with a…
We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This enables us to define some new invariants of smooth projective…
We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of…