## Institut for Matematik ## Hypersurfaces in Pn with 1-parameter symmetry groups II

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### Standard

I: Manuscripta Mathematica, Bind 131, Nr. 1-2, 2010, s. 111-143.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Harvard

Plessis, AD & Wall, CTC 2010, 'Hypersurfaces in Pn with 1-parameter symmetry groups II', Manuscripta Mathematica, bind 131, nr. 1-2, s. 111-143. https://doi.org/10.1007/s00229-009-0304-1

### Author

Plessis, Andrew du ; Wall, C.T.C. / Hypersurfaces in Pn with 1-parameter symmetry groups II. I: Manuscripta Mathematica. 2010 ; Bind 131, Nr. 1-2. s. 111-143.

### Bibtex

@article{727a31c0171f11dfb95d000ea68e967b,
title = "Hypersurfaces in Pn with 1-parameter symmetry groups II",
abstract = "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.",
author = "Plessis, {Andrew du} and C.T.C. Wall",
year = "2010",
doi = "10.1007/s00229-009-0304-1",
language = "English",
volume = "131",
pages = "111--143",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer",
number = "1-2",

}

### RIS

TY - JOUR

T1 - Hypersurfaces in Pn with 1-parameter symmetry groups II

AU - Plessis, Andrew du

AU - Wall, C.T.C.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

U2 - 10.1007/s00229-009-0304-1

DO - 10.1007/s00229-009-0304-1

M3 - Journal article

VL - 131

SP - 111

EP - 143

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1-2

ER -