63 research outputs found
Topological types of real regular jacobian elliptic surfaces
We present the topological classification of real parts of real regular
elliptic surfaces with a real section.Comment: 17 pages, 7 figures, to appear in Geometriae Dedicat
Cremona transformations and diffeomorphisms of surfaces
We show that the action of Cremona transformations on the real points of
quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the
torus, and of all non-orientable surfaces. The main result says that if X is
rational, then Aut(X), the group of algebraic automorphisms, is dense in
Diff(X), the group of self-diffeomorphisms of X.Comment: 17 pages, 11 figures, shorter proofs and improvement of the result
Fake Real Planes: exotic affine algebraic models of
We study real rational models of the euclidean affine plane
up to isomorphisms and up to birational diffeomorphisms. The analogous study in
the compact case, that is the classification of real rational models of the
real projective plane is well known: up to
birational diffeomorphisms, is the only model. A
fake real plane is a smooth geometrically integral surface defined over
not isomorphic to , whose real locus
is diffeomorphic to and such that the complex
surface has the rational homology type of
. We prove that fake planes exist by giving many
examples and we tackle the question: does there exist fake planes such that
is not birationally diffeomorphic to
?Comment: 36 pages, 18 figure
Real frontiers of fake planes
In [8], we define and partially classify fake real planes, that is, minimal
complex surfaces with conjugation whose real locus is diffeomorphic to the
euclidean real plane . Classification results are given up to
biregular isomorphisms and up to birational diffeomorphisms. In this note, we
describe in an elementary way numerous examples of fake real planes and we
exhibit examples of such planes of every Kodaira dimension which are birationally diffeomorphic to
Every connected sum of lens spaces is a real component of a uniruled algebraic variety
Let M be a connected sum of finitely many lens spaces, and let N be a
connected sum of finitely many copies of S^1xS^2. We show that there is a
uniruled algebraic variety X such that the connected sum M#N of M and N is
diffeomorphic to a connected component of the set of real points X(R) of X. In
particular, any finite connected sum of lens spaces is diffeomorphic to a real
component of a uniruled algebraic variety.Comment: Nouvelle version avec deux figure
The group of automorphisms of a real rational surface is n-transitive
Let X be a rational nonsingular compact connected real algebraic surface.
Denote by Aut(X) the group of real algebraic automorphisms of X. We show that
the group Aut(X) acts n-transitively on X, for all natural integers n. As an
application we give a new and simpler proof of the fact that two rational
nonsingular compact connected real algebraic surfaces are isomorphic if and
only if they are homeomorphic as topological surfaces.Comment: Title changed, exposition improve
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