LEADER 02782nam 2200529 450 001 9910816033003321 005 20200106153957.0 010 $a1-4704-5399-1 035 $a(CKB)4940000000160190 035 $a(MiAaPQ)EBC5990837 035 $a(RPAM)21564451 035 $a(PPN)242522386 035 $a(EXLCZ)994940000000160190 100 $a20200106h20192019 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aQuiver grassmannians of extended Dynkin type D$hPart I$iSchubert systems and decompositions into affien spaces /$fOliver Lorscheid, Thorsten Weist 210 1$aProvidence, RI :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (90 pages) $cillustrations 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vSeptember 2019, volume 261, number 1258 311 $a1-4704-3647-7 320 $aIncludes bibliographical references. 327 $aBackground -- Schubert systems -- First applications -- Schubert decompositions for type Dn -- Proof of Theorem 4.1. 330 $a"Let Q be a quiver of extended Dynkin type Dn. In this first of two papers, we show that the quiver Grassmannian Gre(M) has a decomposition into affine spaces for every dimension vector e and every indecomposable representation M of defect -1 and defect 0, with exception of the non-Schurian representations in homogeneous tubes. We characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution we develop the theory of Schubert systems. In Part 2 of this pair of papers, we extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vvol. 261, no. 1258. 517 3 $aSchubert systems and decompositions into affine spaces 606 $aDynkin diagrams 606 $aGrassmann manifolds 606 $aMathematics 615 0$aDynkin diagrams. 615 0$aGrassmann manifolds. 615 0$aMathematics. 676 $a516.3/52 686 $a13F60$a14F45$a14M15$a14N15$a16G20$a05E10$a14M17$a16G60$2msc 700 $aLorscheid$b Oliver$01703551 702 $aWeist$b Thorsten 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816033003321 996 $aQuiver grassmannians of extended Dynkin type D$94088839 997 $aUNINA