Rational and homological equivalence for real cycles.
Rational points on a subanalytic surface
Let be a compact subanalytic surface. This paper shows that, in a suitable sense, there are very few rational points of that do not lie on some connected semialgebraic curve contained in .
Rational points on algebraic varieties over a generalized real closed field: a model theoretic approach.
Rational real algebraic models of topological surfaces.
Real Abelian Varieties and the Theory of Comessatti.
Real algebraic curves
Real algebraic curves and real algebraic functions.
Real Algebraic Curves as Complete Intersections.
Real algebraic curves in the moduli space of complex curves
Real algebraic curves, the moment map and amoebas.
Real Algebraic Geometry and the 17th Hilbert Problem.
Real algebraic hypersurfaces in complex projective varieties.
Real Algebraic Surfaces with Rational or Elliptic Fiberings.
Real algebraic threefolds I. Terminal singularities.
The aim of this series of papers is to develop the theory of minimal models for real algebraic threefolds. The ultimate aim is to understand the topology of the set of real points of real algebraic threefolds. We pay special attention to 3–folds which are birational to projective space and, more generally, to 3–folds of Kodaira dimension minus infinity.present work contains the beginning steps of this program. First we classify 3–dimensional terminal singularities over any field of characteristic...
Real commutative algebra (I). Places.
Real commutative algebra (II). Plane curves.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Real components of algebraic varieties and étale cohomologie.
Real cubic hypersurfaces and group laws.
Let X be a real cubic hypersurface in Pn. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in Hn-1(Pn(R),Z/2Z). Let L be the set of real linear subspaces L of Pn of dimension n - 2 contained in X such that L(R) ⊆ C. We show that, under certain conditions on X, there is a group law on the set L. It is determined by L + L' + L = 0 in L if and only if there is a real hyperplane H...
Real equivalence of complex matrix pencils and complex projections of real Segre varieties.