Algebraic and Topological Combinatorics

Special Session at the Spring Eastern Section Meeting
of the American Mathematical Society

Courant Institute, New York, NY
April 12-13, 2003



Sergey Yuzvinsky
(University of Oregon)


Realization of Abelian groups by complex plane nets


Abstract:This work is a continuation of the theme from the author's talk at the AMS meeting in October 2001 (abs. #971-05-49). In particular we announce proofs of some conjectures from that talk. This theme appeared from studies of the cohomology jumping loci of projective line arrangements but the present talk is self-contained. One of the main results announced here is as follows. Let G be a finite Abelian group with at least one element of order greater than 9. Then every net of lines in a complex projective plane realizing G is algebraic, i.e., dual to a set of points on a cubic. This implies in particular that if G is realizable by a plane net then G is isomorphic to a subgroup of the 2-dimensional torus.

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last updated: April 3, 2003