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Abstract
We study configurations of 2-planes in 
that are combinatorially described by the Petersen graph. We discuss conditions for configurations to be locally Cohen–Macaulay and describe the Hilbert scheme of such arrangements. An analysis of the homogeneous ideals of these configurations leads, via linkage, to a class of smooth, general type surfaces in . We compute their numerical invariants and show that they have the unusual property that they admit (multiple) 7-secants. Finally, we demonstrate that the construction applied to Petersen arrangements with additional symmetry leads to surfaces with exceptional automorphism groups.
Key words.: Plane arrangements; Petersen graph; automorphisms; 7-secants; general type surface; liaison; group actions; linkage
Received: 2007-06-20
Published Online: 2009-06-30
Published in Print: 2009-July
© de Gruyter 2009
