Elementary modifications and line configurations in P^2

  • Henry K. Schenck

    University of Illinois, Urbana, United States


Associated to a projective arrangement of hyperplanes A{\mathcal A} in P^n is the module D(A)({\mathcal A}), which consists of derivations tangent to A{\mathcal A}. We study D(A)({\mathcal A}) when A{\mathcal A} is a configuration of lines in P^2. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regularity of D(A)({\mathcal A}). We also give simple combinatorial conditions for the associated bundle to be stable, and describe its jump lines. These regularity bounds and stability considerations impose constraints on Teraos conjecture.

Cite this article

Henry K. Schenck, Elementary modifications and line configurations in P^2. Comment. Math. Helv. 78 (2003), no. 3, pp. 447–462

DOI 10.1007/S00014-003-0762-0