Free Subarrangements of Shi Arrangements.

Athanasiadis characterized the freeness of the cones of the arrangements between braid arrangements and Shi arrangements. We are interested in the subarrangements Shi(G) of Shi arrangements associated with a graph G, which may not contain all hyperplanes of braid arrangements. We classify the cones of the arrangements Shi(G) which are free. In the meanwhile, we give the graphical interpretation of the exponents of free arrangements c (Shi(G)). [ABSTRACT FROM AUTHOR]