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.
Real forms of smooth del Pezzo surfaces.
Real Grassmann polylogarithms and Chern classes.
Real hypersurfaces with many simple singularities.
In this paper we present constructions of real hypersurfaces with many simple singularities and deduce an asymptotical optimal existence result for hypersurfaces corresponding to T-smooth germs of the equisingular stratum. We proceed along the lines of Shustin-Westenberge (2004) where analogous results were shown for the complex case.
Real Kodaira surfaces.
In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. Moreover, we use the notion of the orbifold fundamental group of a real variety, which was also the main tool in the classification of real hyperelliptic surfaces achieved in [10]. Our first result is that if (S,sygma) is a real primary Kodaira surface, then the differentiable tupe of the pair (S,sygma) is completely determined by the orbifold...
Real Moduli of Complex Objects: Surfaces and Bundles.
Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in with exponential non-linearity and target a convex body is solvable iff is the barycenter of Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties saying that admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new proof and...
Real points on complex plane curves.
Real projective structures on Riemann surfaces
Real quartic surfaces containing 16 skew lines.
Real Schottky uniformizations and Jacobians of May surfaces.
Given a closed Riemann surface R of genus p ≥ 2 together with an anticonformal involution τ : R ---> R with fixed points, we consider the group K(R, τ) consisting of the conformal and anticonformal automorphisms of R which commute with τ...
Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro.
Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II
Let be a real smooth projective 3-fold fibred by rational curves such that is orientable. J. Kollár proved that a connected component of is essentially either Seifert fibred or a connected sum of lens spaces. Answering three questions of Kollár, we give sharp estimates on the number and the multiplicities of the Seifert fibres (resp. the number and the torsions of the lens spaces) when is a geometrically rational surface. When is Seifert fibred over a base orbifold , our result generalizes...
Real spectra of complete local rings.
Real Structure of Teichmüller spaces.
Real theta-characteristics on real projective curves.
Real Zeros of Positive Semidefinite Forms. I.
Realisierung formaler Gruppen durch Kohomologiefunktoren.