Suppose S is a surface in ℙ3, and p1,...,pr are general points on S. What is the dimension of the space of sections of OS(e) having singularities of multiplicity mi at pi for all i? We formulate two natural conjectures which would answer this question, and we show they are equivalent. We then prove these conjectures in case all multiplicities are at most 4.
All Science Journal Classification (ASJC) codes
- Applied Mathematics