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Since is a simple node, the tangent cone to this point is mapped to a conic under the double cover.
This conic is in fact tangent to the six lines ( w. o proof ).
Conversely, given a configuration of a conic and six lines which tangent to it in the plane, we may define the double cover of the plane ramified over the union of these 6 lines.
This double cover may be mapped to, under a map which blows down the double cover of the special conic, and is an isomorphism elsewhere ( w. o.
proof ).

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