The Poincar\'e-Deligne polynomial of Milnor fibers of triple point line arrangements is combinatorially determined

TL;DR

This paper demonstrates that for certain line arrangements with only double and triple points, the equivariant Poincaré-Deligne polynomial of their Milnor fibers can be determined solely from combinatorial data, leveraging recent results.

Contribution

It establishes the combinatorial determination of the equivariant Poincaré-Deligne polynomial for specific line arrangements, extending understanding of Milnor fibers.

Findings

The polynomial is determined by combinatorial data.

Applicable to arrangements with only double and triple points.

Builds on recent results by Papadima and Suciu.

Abstract

Using a recent result by S. Papadima and A. Suciu, we show that the equivariant Poincar\'e-Deligne polynomial of the Milnor fiber of a projective line arrangement having only double and triple points is combinatorially determined.