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

2006-10-11 13:00 - 2006-10-11 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 line and 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 the ideal of $p_i$.The module D is graded and free of rank 2; the degrees of its homogeneous basis, called the exponents, form an important invariant of the divisor. Our main result asserts that under some conditions for S(m_i)$ there exists a general position of $n$ points for which the exponents do not change. We give an explicit formula for them. This talk is the second in a series of talks whose aim is to prove our main result.