Numerical invariants and moduli spaces for line arrangements

Abstract

Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane curves using the Castelnuovo-Mumford regularity of the associated Milnor/Jacobian algebra.

v3: A new proof of a result due to Tohaneanu, giving the classification of line arrangements with a Jacobian syzygy of minimal degree 2 is given in Theorem 4.11. Some other minor changes