Given a (compact if needed) real smooth surface $V(f)$ defined by $f\in \mathbb{R}[X,Y,Z]$, in particular it is oriented. Is there a formula which gives the Euler character of $V(f)$ ?
Thanks.
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Sign up to join this communityGiven a (compact if needed) real smooth surface $V(f)$ defined by $f\in \mathbb{R}[X,Y,Z]$, in particular it is oriented. Is there a formula which gives the Euler character of $V(f)$ ?
Thanks.
A “formula” is a lot to ask for, but there are algorithms based on Morse theory.
E.g. §5 of Basu (1999), or §3 of Fortuna-Gianni-Luminati (2004).