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We answer a question posed by Fielder in [1] concerning two notions ofcrossing number for algebraic knots $K$ under Hopf fibration, one topological,denoted $h(K)$, the other coming from the realization of such knots aroundcomplex singularities, denoted $C_{alg}(K)$. We show that $C_{alg}(K)-h(K)$ canbe arbitrarily large. We also give an upper bound for $h$ of some families ofknots such as torus knots $T(2,n)$, twist knots and their mirror images.

On two crossing numbers of algebraic knots under Hopf fibration