Giancarlo Urzua, University of Michigan

On line arrangements with applications to 3-nets

First, I will briefly explain my motivations to study arrangements of curves on algebraic surfaces. Then, I will concentrate on line arrangements in P^2. I will show a one to one correspondence between pairs (A,p), where A is an arrangement of d lines and p is a point outside of A, and lines in P^{d-2} outside of a fixed hyperplane arrangement. I will show this via moduli spaces of marked genus zero curves. Using this, we are able to obtain a more general correspondence between certain arrangements of d curves, which generalize line arrangements, and certain curves in P^{d-2}. Finally, I will apply this correspondence to prove the existence of some 3-nets in P^2.

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