Hyperplane Arrangement Seminar Derivations of an effective divisor on the complex projective line IV

2006-11-01 13:00 - 2006-11-01 14:30
Room 8-302, Faculty of Science Bldg. #8, Hokkaido University
Max Wakefield (Hokkaido University)
In this talk we consider an effective divisor on the complex projective lineand associate with it the module D consisting of all the derivations $\theta$such that $\theta(I_i)\subset I_i^{m_i}$ for every $i$, where $I_i$ is theideal of $p_i$.The module D is graded and free of rank 2;the degrees of its homogeneous basis, called the exponents, form an importantinvariant of the divisor. Our main result asserts that under some conditionsfor $(m_i)$ there exists a general position of $n$ points for which theexponents do not change. We give an explicit formula for them.This talk is the fourth in a series of talks whose aim it is to prove ourmain result.