An algebraic curve defined by a polynomial of degree n can have at most (n−1)(n−2)/2 singularities. What is the maximal number of singularities of a curve in a k-dimensional space in terms of the degree of the k-1 polynomial equations defining the curve?


P.S.: The comment of Mohan posted below gives an upper bound on the number of singularities by using the fact the the geometric genus is non-negative. So, I could reformulate my question as follows. Are there space curves of genus 0 (or 1) so that the upper bound (possibly minus 1) is attained? given for granted that the curve is irreducible. 



Maximal number of singularities of an algebraic curve
The maximum number of singularities, properly counted, is equal to the arithmetic genus. For example, take the curve $x\_1^2=x\_2,\, x\_2^2=x\_3,\dots,x\_{k-1}^2=x\_k$. This curve has a rational parametrization. Thus, the geometric genus is equal to zero and the number of singularities (at infinity) is equal to the arithmetic genus.


