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Hypersurfaces in Pn with 1-parameter symmetry groups II
Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review
- Andrew du Plessis
- C.T.C. Wall, University of Liverpool, Storbritannien
- Institut for Matematiske Fag
We assume V a hypersurface of degree d in 
with isolated singularities and not a cone, admitting a group G of linear symmetries. In earlier work we treated the case when G is semi-simple; here we analyse the unipotent case. Our first main result lists the possible groups G. In each case we discuss the geometry of the action, reduce V to a normal form, find the singular points, study their nature, and calculate the Milnor numbers. The Tjurina number τ(V) ≤ (d − 1) n–2(d 2 − 3d + 3): we call V oversymmetric if this value is attained. We calculate τ in many cases, and characterise the oversymmetric situations. In particular, we list all the cases with dim(G) = 2 which are the oversymmetric cases with d = 3.
with isolated singularities and not a cone, admitting a group G of linear symmetries. In earlier work we treated the case when G is semi-simple; here we analyse the unipotent case. Our first main result lists the possible groups G. In each case we discuss the geometry of the action, reduce V to a normal form, find the singular points, study their nature, and calculate the Milnor numbers. The Tjurina number τ(V) ≤ (d − 1) n–2(d 2 − 3d + 3): we call V oversymmetric if this value is attained. We calculate τ in many cases, and characterise the oversymmetric situations. In particular, we list all the cases with dim(G) = 2 which are the oversymmetric cases with d = 3.| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Manuscripta Mathematica |
| Vol/bind | 131 |
| Nummer | 1-2 |
| Sider (fra-til) | 111-143 |
| Antal sider | 33 |
| ISSN | 0025-2611 |
| DOI | |
| Status | Udgivet - 2010 |
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