Spectrum of projective plane curve arrangements with ordinary singularities

Abstract

The Hodge spectrum is an important analytic invariant of singularities encoding the Hodge filtration and the monodromy of the Milnor fiber. However, explicit formulas exist in only a few cases. In this article, the main result is a combinatorial formula for the Hodge spectrum of any homogeneous polynomials in three variables whose zero locus is a projective curve arrangement having only ordinary multiple points.

Keywords:

• Hodge spectrum
• hypersurface arrangements
• spectrum formula
• singularities

Mathematics Subject Classification 2010:

• 14B05

Acknowledgments

The author would like to thank Nero Budur and Alexander Dimca for suggesting this problem to me, as well as Gabriel C. Drummond-Cole and Xia Liao for useful comments.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) (No. NRF-2017R1C1B1005166).