Logarithmic vector fields for quasihomogeneous curve configurations in P^2
Abstract
Let A be a union of smooth plane curves C_i, such that each singular point of A is quasihomogeneous. We prove that if C is a smooth curve such that each singular point of A U C is also quasihomogeneous, then there is an elementary modification of rank two bundles, which relates the O_{P^2} module Der(log A) of vector fields on P^2 tangent to A to the module Der(log A U C). This yields an inductive tool for studying the splitting of the bundles Der(log A) and Der(log A U C), depending on the geometry of the divisor A_C on C.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.3237
 Bibcode:
 2014arXiv1407.3237S
 Keywords:

 Mathematics  Algebraic Geometry;
 Primary 52C35;
 Secondary 14J60
 EPrint:
 10 pages 2 figures