The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
Real cubic hypersurfaces and group laws.
Let X be a real cubic hypersurface in P. 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 H(P(R),Z/2Z). Let be the set of real linear subspaces L of P 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 . It is determined by L + L' + L = 0 in if and only if there is a real hyperplane H in P such...
Unramified nonspecial real space curves having many real branches and few ovals.
Let C ⊆ P be an unramified nonspecial real space curve having many real branches and few ovals. We show that C is a rational normal curve if n is even, and that C is an M-curve having no ovals if n is odd.
Every connected sum of lens spaces is a real component of a uniruled algebraic variety
We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.
On the enumerative geometry of real algebraic curves having many real branches.
Inflection points on real plane curves having many pseudo-lines.
Rational real algebraic models of topological surfaces.
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