LEADER 04558nam 2200649 450 001 996466772203316 005 20220305004338.0 010 $a3-540-47851-5 024 7 $a10.1007/BFb0078834 035 $a(CKB)1000000000437532 035 $a(SSID)ssj0000326671 035 $a(PQKBManifestationID)12061285 035 $a(PQKBTitleCode)TC0000326671 035 $a(PQKBWorkID)10296523 035 $a(PQKB)11762892 035 $a(DE-He213)978-3-540-47851-5 035 $a(MiAaPQ)EBC5610979 035 $a(Au-PeEL)EBL5610979 035 $a(OCoLC)1079006967 035 $a(MiAaPQ)EBC6842704 035 $a(Au-PeEL)EBL6842704 035 $a(OCoLC)1292357139 035 $a(PPN)155176633 035 $a(EXLCZ)991000000000437532 100 $a20220305d1987 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aSingularities, representation of algebras, and vector bundles $eproceedings of a symposium held in Lambrecht/Pfalz, Fed. Rep. of Germany, Dec. 13-17, 1985 /$fedited by Gert-Martin Greuel and Gu?nther Trautmann 205 $a1st ed. 1987. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1987] 210 4$d©1987 215 $a1 online resource (XVI, 384 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1273 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-18263-2 327 $aSurvey of vector bundles on curves -- Finite and countable CM-representation type -- Finite dimensional algebras and singularities -- Cohen-Macaulay modules on quadrics -- Monomial curves and obstructions on cyclic quotient singularities -- The Grothendieck group of invariant rings and of simple hypersurface singularities -- Torsionsfreie Moduln bei Deformation von Kurvensingularitäten -- Deformation of modules on curves and surfaces -- A characterisation of strictly unimodular plane curve singularities -- Polar curves, resolution of singularities and the filtered mixed hodge structure on the vanishing cohomology -- On the betti numbers of the milnor fibre of a certain class of hypersurface singularities -- Reflexive modules on cyclic quotient surface singularities -- Almost split sequences for ?-graded rings -- The auslander-reiten quiver of an isolated singularity -- A class of weighted projective curves arising in representation theory of finite dimensional algebras -- Repetitive categories -- Almost split sequences for some non-classical lattice categories -- Special instanton bundles and poncelet curves -- Groupe de picard des variétés de modules de faisceaux semi-stables sur ?2 -- On the rationality of the moduli space for stable rank-2 vector bunoles on P2 -- A theorem on zero schemes of sections in two-bundles over affine schemes with applications to set theoretic intersections. 330 $aIt is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1273 606 $aVector bundles$vCongresses 606 $aRepresentations of algebras$vCongresses 606 $aSingularities (Mathematics)$vCongresses 615 0$aVector bundles 615 0$aRepresentations of algebras 615 0$aSingularities (Mathematics) 676 $a512.5 702 $aGreuel$b Gert-Martin 702 $aTrautmann$b Gu?nther 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466772203316 996 $aSingularities, representation of algebras, and vector bundles$979899 997 $aUNISA