Loading...
Please wait, while we are loading the content...
Similar Documents
Sheaves on projective space invariant under the unitriangular group
| Content Provider | Semantic Scholar |
|---|---|
| Author | Horrocks, Geoffrey C. |
| Copyright Year | 1970 |
| Abstract | from the category of locally noetherian preschemes over S to the category of sets by taking Q(:W/X/S) T to be the set of flat coherent quotient sheaves of :wr (the sheaf obtained from :W by the base extension T ~ S); he has also shown that Q (:w/X/S) is represented by a scheme Q (:w/x/s) and that those quotients with Hilbert polynomial p correspond to the points of a subscheme Qp(:W/X/S) projective over S. Suppose that a group scheme G over S acts on X and that :W has a G-linearization. Then G acts on Q(:W/X/S) and, with slight restrictions on G, the fixed point subscheme Q(:W/X/S) ~ exists and is closed. This paper is concerned with a fibring of Q (:w/X/S) ~ that exists when X is P", the n-dimensional projective space over S, and G, :W satisfy certain conditions (fulfilled, for example, by the unitriangular group and the sheaf of local rings of P"). The fibring is given by a morphism f(:w) of Q(:W/P"/S) ~ into a scheme Q(.WIP"-llS) ~ which maps Qp into Qn~, where A p is the first difference p ( x ) p (x 1). The fibres of the component fP(:W) of f( :w) are simply connected when the fibres of G over S have composition series with factors that are additive groups; fP(:w) is surjective if p(0) is sufficiently large (ap and :W being fixed) and the fibres of G over S are solvable. For the special case of the Hilbert schemes Hilb (P"/S) these results show that Hill~' (P/S) is universally 1-connected relative to S (see w 5) if p is a polynomial of degree at most n 1 such that the ASp(O) are integers satisfying |
| Starting Page | 108 |
| Ending Page | 118 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BF01403150 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/BF01403150 |
| Alternate Webpage(s) | https://doi.org/10.1007/BF01403150 |
| Volume Number | 10 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
