Let $X$ ba an algebraic variety and $\mathrm{Sing}(X)$ be the set of all singular points.
For a set $A$ , $|A|$ denotes the cardinality of $A$ .
I konw examples of algebraic variety with finite singularities.
But I cannot get algebraic varieties which have infinitely many singularities.
I have following questions.
My questions
$(1)$ Can you construct algebraic varieties $X$ satisfying $|\mathrm{Sing}(X)|=|\mathbb{R}|$ $??$
$(2)$ Can you construct algebraic varieties $Y$ satisfying $|\mathrm{Sing}(Y)|=|\mathbb{Q}|$ $??$