Related papers: Unobstructedness of deformations of weak Fano mani…

We prove birational superrigidity of Fano double hypersurfaces of index one with quadratic and multi-quadratic singularities, satisfying certain regularity conditions, and give an effective explicit lower bound for the codimension of the…

I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q>0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo…

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…

We study unirationality of actions of finite groups on Fano threefolds.

We show that the set of Fano varieties (with arbitrary singularities) whose anticanonical divisors have large Seshadri constants satisfies certain weak and birational boundedness. We also classify singular Fano varieties of dimension $n$…

The Debarre-de Jong conjecture predicts that the Fano variety of lines on a smooth Fano hypersurface in $\mathbb{P}^n$ is always of the expected dimension. We generalize this conjecture to the case of Fano complete intersections and prove…

In this paper, we study the structure of Fano fibrations of varieties admitting an int-amplified endomorphism. We prove that if a normal $\mathbb{Q}$-factorial klt projective variety $X$ has an int-amplified endomorphism, then there exists…

This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of…

For a smooth curve $B$ over an algebraically closed field $k$, for every $B$-flat complete intersection $X_B$ in $B\times_{\text{Spec}\ k} \mathbb{P}^n_k$ of type $(d_1,\dots,d_c)$, if the Fano index is $\geq 2$ and if…

A projective variety has a large fundamental group if its universal covering has no compact subvarieties. In this paper we investigate whether the property of a variety having a large fundamental groups is stable under K\"{a}hler…

The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.

Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its relationship with other convergences. In particular, we…

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…

We study cohomological obstructions to equivariant unirationality, with special regard to actions of finite groups on del Pezzo surfaces and Fano threefolds.

We observe a method for finding weak Landau-Ginzburg models for Fano varieties and find them for smooth Fano threefolds of genera 9, 10, and 12.

We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic.

In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

This note is about cycle-theoretic properties of the Fano variety of lines on a smooth cubic fivefold. The arguments are based on the fact that this Fano variety has finite-dimensional motive. We also present some results concerning Chow…

We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of compact complex symplectic manifolds, obtaining some…