Related papers: On smooth projective D-affine varieties

We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection $\nabla$ on a compact complex surface is locally modelled on a translations-invariant…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

We generalize the construction of Raynaud of smooth projective surfaces of general type in positive characteristic that violate the Kodaira vanishing theorem. This corrects an earlier paper of the same purpose. These examples are smooth…

Consider a finite morphism f:X -> Y of smooth projective varieties over a finite field k. Suppose X is the vanishing locus in projective N-space of at most r forms of degree at most d. We show there is a constant C, depending only on N, r,…

In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved or almost nef. Specifically, we show that such a variety $X$,…

We classify the d-dimensional simplicial, terminal, and reflexive polytopes with at least 3d-2 vertices. In particular, it turns out that these are all smooth Fano polytopes. This improves on previous results of Casagrande in 2006 and Oebro…

Fix a number field k. We prove that if there is an algorithm for deciding whether a smooth projective geometrically integral k-variety has a k-point, then there is an algorithm for deciding whether an arbitrary k-variety has a k-point and…

Let $X$ be a smooth projective variety defined over an algebraically closed field, and let $L$ be an ample line bundle over $X$. We prove that for any smooth hypersurface $D$ on $X$ in the complete linear system $| L^{\otimes d}|$, the…

For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic D-module (M, F) on the dual projective space. This gives a concrete description of the…

We prove that a smooth projective variety of dimension n is isomorphic to projective n-space iff the canonical class is -(n+1)-times an ample divisor. In characteristic zero this was proved by Kobayashi-Ochiai. We also extend the second…

A well-known theorem of W. Fischer and H. Grauert states that analytic fiber spaces with all fibers isomorphic to a fixed compact connected complex manifold are locally trivial. Motivated by this result, we show that if $k$ is an…

We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…

In this short note we give a characterization of smooth projective varieties of Picard number one that are separably uniruled but not separably rationally connected. We also give a sufficient condition involving the torsion order and the…

We discuss the isomorphism problem of projective schemes; given two projective schemes, can we algorithmically decide whether they are isomorphic? We give affirmative answers in the case of one-dimensional projective schemes, the case of…

In this study, we introduce a new type of surface curves called D-type curve. This curve is defined by the property that the unit Darboux vector W0 of a space curve r(s) and unit surface normal n along the curve r(s) satisfy the condition…

We prove that smooth projective varieties with equivalent derived categories have isogenous (and sometimes isomorphic) Picard varieties. In particular their irregularity and number of independent vector fields are the same. This is turn…

This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…

Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$ fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as a fibration over an abelian variety whose fibers are isomorphic to a product of…

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.

In the present paper we discuss coherent sheaves of rank > 1 whose projectivization gives rise to smooth varieties - varieties of this type are also called smooth scrolls. We prove some basic properties of these varieties and we give some…