# Surfaces in $\mathbb P^3$ with many simple isolated singularities

Could anybody help me with examples of surfaces $X\subset\mathbb P^3$ (projective, over $\mathbb C$) having many isolated singularities of the type $A_1$ ($x^2+y^2+z^2=0$) or $A_2$ ($x^2+y^2+z^3=0$) and no other singular points? «Many» means «as close to the known upper bound (in terms of $\deg X$) as possible».

Thank you in advance,
Serge

• For nodal surfaces, maybe this site would help oliverlabs.net/view.php?menuitem=168 – BS. Aug 16 '13 at 15:34
• What is the known upper bound? – Mariano Suárez-Álvarez Aug 16 '13 at 19:59
• There is a nice paper by Bruce and Wall that might be of interest to you, in which they classify all possible singularities which may occur for cubic surfaces. – Daniel Loughran Aug 16 '13 at 20:47

For the case of surfaces of degree $\le 6$, you may consult Catanese, F.; Ceresa, G.: J. Pure Appl. Algebra 23 (1982), and, if you read Italian,