TY - JOUR
AU - Viu-Sos, Juan
AB - Abstract:This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate combinatorial classes of arrangements whose moduli space is connected. We unify the classes of simple and inductively connected arrangements appearing in the literature. Then, we introduce the notion of arrangements with a rigid pencil form. It ensures the connectedness of the moduli space and is less restrictive that the class of $C_3$ arrangements of simple type. In the last part, we obtain a combinatorial upper bound on the number of connected components of the moduli space. Then, we exhibit examples with an arbitrarily large number of connected components for which this upper bound is sharp.
TI - Connectedness and combinatorial interplay in the moduli space of line arrangements
JF - Mathematics
DO - 10.48550/arxiv.2309.00322
DA - 2023-09-01
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/connectedness-and-combinatorial-interplay-in-the-moduli-space-of-line-81uCgESdds
VL - 2024
IS - 2309
DP - DeepDyve
ER -