FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1986006973> ?p ?o ?g. }

• W1986006973 endingPage "506" @default.
• W1986006973 startingPage "491" @default.
• W1986006973 abstract "The study of reductive group actions on a normal surface singularity X is facilitated by the fact that the group Aut X of automorphisms of X has a maximal reductive algebraic subgroup G which contains every reductive algebraic subgroup of Aut X up to conjugation. If X is not weighted homogeneous then this maximal group G is finite (Scheja, Wiebe). It has been determined for cusp singularities by Wall. On the other hand, if X is weighted homogeneous but not a cyclic quotient singularity then the connected component G1 of the unit coincides with the C* defining the weighted homogeneous structure (Scheja, Wiebe, Wahl). Thus the main interest lies in the finite group G/G1. Not much is known about G/G1. Ganter has given a bound on its order valid for Gorenstein singularities which are not log-canonical. Aumann-Körber has determined G/G1 for all quotient singularities. We propose to study G/G1 through the action of G on the minimal good resolution X̂ of X. If X is weighted homogeneous but not a cyclic quotient singularity, let E0 be the central curve of the exceptional divisor of X̂. We show that the natural homomorphism G→Aut E0 has kernel C* and finite image. In particular, this re-proves the rest of Scheja, Wiebe and Wahl mentioned above. Moreover, it allows us to view G/G1 as a subgroup of Aut E0. For simple elliptic singularities it equals (Zb×Zb)⋊Aut0 E0 where −b is the self-intersection number of E0, Zb×Zb is the group of b-torsion points of the elliptic curve E0 acting by translations, and Aut0 E0 is the group of automorphisms fixing the zero element of E0. If E0 is rational then G/G1 is the group of automorphisms of E0 which permute the intersection points with the branches of the exceptional divisor while preserving the Seifert invariants of these branches. When there are exactly three branches we conclude that G/G1 is isomorphic to the group of automorphisms of the weighted resolution graph. This applies to all non-cyclic quotient singularities as well as to triangle singularities. We also investigate whether the maximal reductive automorphism group is a direct product G≃G1×G/G1. This is the case, for instance, if the central curve E0 is rational of even self-intersection number or if X is Gorenstein such that its nowhere-zero 2-form ω has degree ±1. In the latter case there is a ‘natural’ section G/G1↪G of G↪G/G1 given by the group of automorphisms in G which fix ω. For a simple elliptic singularity one has G≃G1×G/G1 if and only if −E0 · E0 = 1." @default.
• W1986006973 created "2016-06-24" @default.
• W1986006973 creator A5046869305 @default.
• W1986006973 date "1999-04-01" @default.
• W1986006973 modified "2023-10-16" @default.
• W1986006973 title "Symmetries of Surface Singularities" @default.
• W1986006973 cites W1523119859 @default.
• W1986006973 cites W1564406588 @default.
• W1986006973 cites W1568270275 @default.
• W1986006973 cites W1616106019 @default.
• W1986006973 cites W1968672921 @default.
• W1986006973 cites W1984090935 @default.
• W1986006973 cites W1991005788 @default.
• W1986006973 cites W1996300040 @default.
• W1986006973 cites W1998311746 @default.
• W1986006973 cites W2007530960 @default.
• W1986006973 cites W2018359545 @default.
• W1986006973 cites W2018897689 @default.
• W1986006973 cites W2024374236 @default.
• W1986006973 cites W2033328505 @default.
• W1986006973 cites W2040676707 @default.
• W1986006973 cites W2061601093 @default.
• W1986006973 cites W2068360288 @default.
• W1986006973 cites W2144219782 @default.
• W1986006973 cites W2161958504 @default.
• W1986006973 cites W2313076269 @default.
• W1986006973 cites W2317861396 @default.
• W1986006973 cites W2335579323 @default.
• W1986006973 cites W2586435699 @default.
• W1986006973 cites W2600793504 @default.
• W1986006973 cites W3144205924 @default.
• W1986006973 cites W3535678 @default.
• W1986006973 doi "https://doi.org/10.1112/s0024610799007188" @default.
• W1986006973 hasPublicationYear "1999" @default.
• W1986006973 type Work @default.
• W1986006973 sameAs 1986006973 @default.
• W1986006973 citedByCount "4" @default.
• W1986006973 countsByYear W19860069732013 @default.
• W1986006973 countsByYear W19860069732014 @default.
• W1986006973 crossrefType "journal-article" @default.
• W1986006973 hasAuthorship W1986006973A5046869305 @default.
• W1986006973 hasBestOaLocation W19860069732 @default.
• W1986006973 hasConcept C10138342 @default.
• W1986006973 hasConcept C114614502 @default.
• W1986006973 hasConcept C121332964 @default.
• W1986006973 hasConcept C12843 @default.
• W1986006973 hasConcept C134306372 @default.
• W1986006973 hasConcept C16171025 @default.
• W1986006973 hasConcept C162324750 @default.
• W1986006973 hasConcept C182306322 @default.
• W1986006973 hasConcept C199422724 @default.
• W1986006973 hasConcept C202444582 @default.
• W1986006973 hasConcept C2524010 @default.
• W1986006973 hasConcept C2777404646 @default.
• W1986006973 hasConcept C2781311116 @default.
• W1986006973 hasConcept C33923547 @default.
• W1986006973 hasConcept C62520636 @default.
• W1986006973 hasConcept C96469262 @default.
• W1986006973 hasConceptScore W1986006973C10138342 @default.
• W1986006973 hasConceptScore W1986006973C114614502 @default.
• W1986006973 hasConceptScore W1986006973C121332964 @default.
• W1986006973 hasConceptScore W1986006973C12843 @default.
• W1986006973 hasConceptScore W1986006973C134306372 @default.
• W1986006973 hasConceptScore W1986006973C16171025 @default.
• W1986006973 hasConceptScore W1986006973C162324750 @default.
• W1986006973 hasConceptScore W1986006973C182306322 @default.
• W1986006973 hasConceptScore W1986006973C199422724 @default.
• W1986006973 hasConceptScore W1986006973C202444582 @default.
• W1986006973 hasConceptScore W1986006973C2524010 @default.
• W1986006973 hasConceptScore W1986006973C2777404646 @default.
• W1986006973 hasConceptScore W1986006973C2781311116 @default.
• W1986006973 hasConceptScore W1986006973C33923547 @default.
• W1986006973 hasConceptScore W1986006973C62520636 @default.
• W1986006973 hasConceptScore W1986006973C96469262 @default.
• W1986006973 hasIssue "2" @default.
• W1986006973 hasLocation W19860069731 @default.
• W1986006973 hasLocation W19860069732 @default.
• W1986006973 hasOpenAccess W1986006973 @default.
• W1986006973 hasPrimaryLocation W19860069731 @default.
• W1986006973 hasRelatedWork W1976722377 @default.
• W1986006973 hasRelatedWork W1979605443 @default.
• W1986006973 hasRelatedWork W2883517507 @default.
• W1986006973 hasRelatedWork W2951295119 @default.
• W1986006973 hasRelatedWork W2955038244 @default.
• W1986006973 hasRelatedWork W2962943933 @default.
• W1986006973 hasRelatedWork W3106212824 @default.
• W1986006973 hasRelatedWork W4200431040 @default.
• W1986006973 hasRelatedWork W4300032282 @default.
• W1986006973 hasRelatedWork W4320489103 @default.
• W1986006973 hasVolume "59" @default.
• W1986006973 isParatext "false" @default.
• W1986006973 isRetracted "false" @default.
• W1986006973 magId "1986006973" @default.
• W1986006973 workType "article" @default.