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Seminario Dottorato: “On the Alexander polynomial of line arrangements in P^2”

Wednesday 27 February 2019, h.14:30 - Room 2BC30 - Federico Venturelli

ARGOMENTI: Seminars Ph.D. Program

Wednesday 27 February 2019 h.14:30, Room 2BC30
Federico Venturelli (Padova, Dip. Mat.)
“On the Alexander polynomial of line arrangements in P^2”

Abstract
The Alexander polynomial was first introduced in the context of knot theory, and it was used to study the local topology of plane curve singularities; this notion was later extended to projective hypersurfaces (zero loci of a single polynomial equation in a projective space), which is the case that will be discussed in this talk. The Alexander polynomial of a hypersurface V encodes information on the monodromy eigenspaces of H^1(F,C), where F is the Milnor fibre of V; while these eigenspaces are well understood for smooth hypersurfaces, they are significantly harder to compute if the hypersurface is singular, even in the simplest cases i.e. hyperplane arrangements.
In my talk I will try to give a basic introduction to this problem, explaining how the combinatorics of a hyperplane arrangement can help in determining its Alexander polynomial and presenting some known results; throughout the exposition some detours will be made, in order to discuss explicit examples and to introduce (or clarify) concepts that could be unfamiliar to non-specialists.

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