Related papers: Solvable points on smooth projective varieties
We show that any smooth one-dimensional link in the real projective three-plane is the fixed-point locus of a smooth symplectic surface in the complex projective three-plane which is invariant under complex conjugation. The degree of the…
We prove that the Quot-scheme of finite quotients of a vector bundle which are of a given length and supported in one point, is irreducible and of the expected dimension.
We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric…
When a non-singular complex projective surface $X$ satisfies that $K_X\sim 0$, we shall show that there are only finitely many isomorphic classes as abstract schemes in the set of moduli scheme of $H$-semistable sheaves with fixed Chern…
We classify indecomposable non-projective Gorenstein-projective modules over a monomial algebra via the notion of perfect paths. We apply this classification to a quadratic monomial algebra and describe explicitly the stable category of its…
We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to this problem would be incompatible with the validity of the…
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted…
For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for…
We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety…
We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.
In this article, we prove an extension property of semipositively metrized ample invertible sheaves on a projective scheme over a complete non-archimedean valued field. As an application, we establish a Nakai-Moishezon type criterion for…
A result of Beauville states that with a few positive characterstic exceptions, the smooth hyperplane sections of hypersurfaces of degree $d>2$ in projective space are not all isomorphic. We address the question of whether these sections…
We show that a smooth Moishezon space $Y$ is non-projective if and only if it contains a rational curve such that $-[C] \in \overline{\mathrm{NE}}(Y)$. More generally, this holds if $Y$ has $\mathbb{Q}$-factorial, log terminal…
We show that pointlike sets are decidable for the pseudovariety of finite semigroups whose idempotent-generated subsemigroup is R-trivial. Notably, our proof is constructive: we provide an explicit relational morphism which computes the…
We show that there are no non-trivial stratified bundles over a smooth simply connected quasi-projective variety over the algebraic closure of a finite field, if the variety admits a normal projective compactification with boundary locus of…
In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…
We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such that \bar{B} - B is of codimension at least two in \bar{B}.…
In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative…