Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten
Ueber die Vieltheiligkeit der ebenen algebraischen Curven
Une inégalité de Lojasiewicz effective
Une sextique de l'espace projectif réel avec un grand nombre d'anses.
It follows from the known restrictions on the topology of a real algebraic variety that the number of handles of the real part of a real nonsingular sextic in CP3 is at most 47. We construct a real nonsingular sextic X6 in CP3 whose real part RX6 has 44 handles. In particular, this surface verifies b1(RX6) = h1,1(X6) + 2. We extend the construction in order to obtain for any even m ≥ 6 a real nonsingular surface Xm of degree m in CP3 verifying b1(RXm) > h1,1(Xm). It is known that such a surface...
Uniformization of rigid subanalytic sets
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.