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- W2034850154 abstract "Let $X_m$ be a nonsingular real algebraic surface of degree m in the complex projective space ${mathbb C}P^3$ and ${mathbb R}X_m$ its real point set in ${mathbb R}P^3$. In the spirit of the sixteenth Hilbert's problem, one can ask for each degree m about the maximal possible value $beta_{i,m}$ of the Betti number $b_i({mathbb R}X_m)$ (i=0 or 1). We show that $beta_{i,m}$ is asymptotically equivalent to $l_i cdot m^3$ for some real number $l_i$ and prove inequalities $frac{13}{36} leq l_0 leq frac{5}{12}$ and $frac{13}{18} leq l_1 leq frac{5}{6}$." @default.
- W2034850154 created "2016-06-24" @default.
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- W2034850154 date "2003-01-01" @default.
- W2034850154 modified "2023-10-13" @default.
- W2034850154 title "Asymptotic behaviour of Betti numbers of real algebraic surfaces" @default.
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- W2034850154 doi "https://doi.org/10.1007/s000140300010" @default.
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