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On Plane Curves with Double and Triple Points

Nancy Abdallah

Abstract


We describe in simple geometric terms the Hodge filtration on the cohomology $H^*(U)$ of the complement $U=\mathsf{P}^2 \setminus C$ of a plane curve $C$ with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration on $H^2(U)$ are given.

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DOI: http://dx.doi.org/10.7146/math.scand.a-24184

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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