Let be a nonsingular real algebraic surface of degree m in the complex projective space and its real point set in . In the spirit of the sixteenth Hilbert's problem, one can ask for each degree m about the maximal possible value of the Betti number (i=0 or 1). We show that is asymptotically equivalent to for some real number and prove inequalities and .
Cite this article
F. Bihan, Asymptotic behaviour of Betti numbers of real algebraic surfaces. Comment. Math. Helv. 78 (2003), no. 2, pp. 227–244DOI 10.1007/S000140300010