score:2

Accepted answer

A dynamic approach to this is intercepting the setState-function of the Point.

For example, wrapping it and preventing the handling if the y-value is 0:

(function (H) {
  H.wrap(H.Point.prototype, 'setState', function (proceed, state, move) {
    if(this.y === 0) return;
    proceed.apply(this, Array.prototype.slice.call(arguments, 1));
  });
}(Highcharts));

See this JSFiddle demonstration of it in action.

score:3

A very static approach to this is simply addressing each point with Y-value of 0. Then you could disable the hover-marker for each of these. One such point would look like this (JSFiddle demo):

{
  y:0, 
  marker:{
    states:{
      hover:{
        enabled:false
      }
    }
  }
}

And used in a series:

series: [{
  marker: {
    enabled: false
  },
  data: [3, {y:0, marker:{states:{hover:{enabled:false}}}}, 3, 5, 1, 2, 12]
}]

As you can see, it's not pretty, but might help those who need an ad-hoc solution.


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