# Publications

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## Surfaces with Many Solitary Points

It is classically known that a real cubic surface in the real projective 3-space cannot have
more than one solitary point (locally
given by x^2+y^2+z^2=0) whereas it can have up
to four nodes (x^2+y^2-z^2=0).
We show that on any surface of degree at least 3 in the real projective 3-space, the maximum
possible number of solitary points is strictly smaller than the maximum
possible number of nodes.
Conversely, we adapt a construction of Chmutov to obtain surfaces with many
solitary points by using a refined version of Brusotti's theorem.
Finally, we adapt this construction to get real algebraic surfaces with many singular points of type $A_{2k-1}^\smbullet$ for all $k\ge 1$.