1. Special linear systems and syzygies
- Author
-
Alberto Alzati
- Subjects
Algebra ,Ideal (set theory) ,Mathematics::Algebraic Geometry ,Mathematics::Complex Variables ,Applied Mathematics ,General Mathematics ,Linear system ,Mathematics::Differential Geometry ,Algebra over a field ,Base locus ,Mathematics - Abstract
Let $X$ be the base locus of a linear system $L$ of hypersurfaces in $\mathbb{P}^r(C)$. In this paper it is showed that the existence of linear syzygies for the ideal of $X$ has strong consequences on the fibres of the rational map associated to $L$. The case of hyperquadrics is particularly addressed. The results are applied to the study of rational maps and to the Perazzo’s map for cubic hypersurfaces.
- Published
- 2008