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.
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.
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