Real plane sextics without real points

We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, i.e., the polarization, exceptional divisors, and real structure recorded in the homology of the covering <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K Baseline 3"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">K3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-surface. As an illustration, we obtain an equisingular deformation classification of real plane sextics with empty real part (for completeness, we consider the few non-simple ones as well).