Coincident root loci of binary forms
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $λ$, let $X_λ$ be the set of forms with root multiplicity corresponding to $λ$. There is a natural action of $GL_2(C)$ on $S^d(C^2)$ and the coincident root loci are invariant under this action. We calculate their equivariant Poincaré duals generalizing formulas of Hilbert and Kirwan. In the second part we apply these results to present the cohomology ring of the corresponding moduli spaces (stable points$/G$, semistable points$/G$, link of the singularity) using geometrically defined relations.
15 pages
15 pages