The complex separation of real surfaces and extensions of Rokhlin congruence.
The geometry of configuration spaces for closed chains in two and three dimensions.
The growth rate of the number of classes of real plane algebraic curves with the growth of the degree.
The Noether-Lefschetz theorem and sums of 4 squares in the rational function field
The number of connected components of certain real algebraic curves.
The principle of moduli flexibility for real algebraic manifolds
Given a real closed field R, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some Rⁿ. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: "The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters".
The underlying real algebraic structure of complex elliptic curves.
Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten
Unramified nonspecial real space curves having many real branches and few ovals.
Let C ⊆ Pn 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.
Welschinger invariants of small non-toric Del Pezzo surfaces
We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at real and pairs of conjugate imaginary points, where , and the real quadric blown up at pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants of real toric...
When is a complex elliptic curve the product of two real algebraic curves?
Witt groups of real projective surfaces.