The flecnode polynomial: a central object in incidence geometry

Abstract

Recently there has been a lot of progress in point/line incidence theory in three dimension real affine spaces. Generally, this progress all happens where the lines and points lie in a ruled surface. Conversely, in many related problems we are yet unable to touch, we are just outside the threshold where the ruled condition can be enforced. This puts the celebrated flecnode polynomial of Cayley and Salmon at the center of the action.

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