Related papers: Hypersurfaces in projective schemes and a moving l…

This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…

We construct the moduli space of smooth hypersurfaces with level $N$ structure over $\mathbb{Z}[1/N]$. As an application we show that, for $N$ large enough, the stack of smooth hypersurfaces over $\mathbb{Z}[1/N]$ is uniformisable by a…

A structure $\cal S$ is quasi-projective if for every structure $\cal T$, for every homomorphism $f : {\cal S} \rightarrow {\cal T}$ and every epimorphism $j: {\cal S}\rightarrow {\cal T}$ there is an endomorphism $\phi$ of $\cal S$ such…

An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator…

We give a general structure theorem for affine A 1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A 1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth…

We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group $\pi_1(X)$ of a compact K\"ahler manifold onto the fundamental group $\Pi_g$ of a compact Riemann surface of…

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle…

This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $\pi_1(X)$ in the presence of a linear representation $\varrho: \pi_1(X) \to {\rm…

Given a closed complex hypersurface $Z\subset \mathbb{C}^{N+1}$ $(N\in\mathbb{N})$ and a compact subset $K\subset Z$, we prove the existence of a pseudoconvex Runge domain $D$ in $Z$ such that $K\subset D$ and there is a complete proper…

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

Let $\pi: X \to Y$ be a morphism of projective varieties and suppose that $\alpha$ is a pseudo-effective numerical cycle class satisfying $\pi_*\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha$ is a limit of…

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

Given a Henselian and Japanese discrete valuation ring $A$ and a flat and projective $A$-scheme $X$, we follow the approach of Biswas-dos Santos to introduce a full subcategory of coherent modules on $X$ which is then shown to be Tannakian.…

We construct a new class of affine complements ${\mathbb P}^M\setminus S$ with the trivial group of automorphisms, where $S\subset {\mathbb P}^M$ is a rational hypersurface, $M$ is odd and $M\geqslant 5$.

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

Let $X$ be a hypersurface in $\mathbb{P}^N$ with $N\geq 3$ defined over a finite field. The main result of this note is the classification, up to projective equivalence, of hypersurfaces $X$ as above without a linear component when the…

We introduce an infinite variant of hypersurface support for finite-dimensional, noncommutative complete intersections. By a noncommutative complete intersection we mean an algebra R which admits a smooth deformation $Q\to R$ by a…

We generalize the functorial quasi-isomorphism in \cite{Davis2011} from overconvergent Witt de-Rham cohomology to rigid cohomology on smooth varieties over a finite field $k$, dropping the quasi-projectiveness condition. We do so by…

Let $X$ be any scheme defined over a Dedekind scheme $S$ with a given section $x\in X(S)$. We prove the existence of a pro-finite $S$-group scheme $\aleph(X,x)$ and a universal $\aleph(X,x)$-torsor dominating all the pro-finite pointed…