On Rao's theorems and the Lazarsfeld-Rao property
On rational torsion points of central -curves
Let be a central -curve over a polyquadratic field . In this article we give an upper bound for prime divisors of the order of the -rational torsion subgroup (see Theorems 1.1 and 1.2). The notion of central -curves is a generalization of that of elliptic curves over . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].
On real algebraic vector bundles.
On real flag manifolds with cup-length equal to its dimension
We prove that for any positive integers there exists a real flag manifold with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.
On reconstructing algebraic sets and ideals
We generalize some results on reconstructing sets to the case of ideals of 𝕜[X₁,...,Xₙ]. We show that reconstructing sets can be approximated by finite subsets having the property of reconstructing automorphisms of bounded degree.
On reconstruction of polynomial automorphisms
We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
On reduction of Hilbert-Blumenthal varieties
Let be the ring of integers of a totally real field of degree . We study the reduction of the moduli space of separably polarized abelian -varieties of dimension modulo for a fixed prime . The invariants and related conditions for the objects in the moduli space are discussed. We construct a scheme-theoretic stratification by -types on the Rapoport locus and study the relation with the slope stratification. In particular, we recover the main results of Goren and Oort [J. Alg. Geom.,...
On reflexive sheaves with low sectional genera on threefolds.
On regular threefolds with k = 0.
On Reider's method for surfaces in positive characterstic.
On relations of invariants for vector-valued forms.
On relative canonical sheaves of arithmetic surfaces.
On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
On representations of with algebras of invariants being complete intersections.
On Rings admitting orderings and 2-primary chains of orderings of higher level.
On rings of semialgebraic functions.
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On Schubert Varieties in the Flag Manifold of SI (n, C).
On secant spaces to projective curves
On second fundamental forms of projective varieties.