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010 a| 2020023140;

020 a| 9781470436476q| (paperback);

020 z| 9781470454005q| (ebook);

035 a| (WaSeSS)ssj0002325411;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA251.3b| .L67 2019;

082 00 a| 516.3/522| 23;

084 a| 13F60a| 14F45a| 14M15a| 14N15a| 16G20a| 05E10a| 14M17a| 16G602| msc;

100 1 a| Lorscheid, Oliver.?| UNAUTHORIZED;

245 10 a| Quiver grassmannians of extended Dynkin type Dh| [electronic resource] :b| part I : Schubert systems and decompositions into affine spaces /c| Oliver Lorscheid, Thorsten Weist.;

246 30 a| Schubert systems and decompositions into affine spaces;

260 a| Providence, RI :b| American Mathematical Society,c| 2019.;

300 a| v, 78 pages :b| illustrations ;c| 25 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1258;

504 a| Includes bibliographical references (pages 77-78).;

505 0 a| Background -- Schubert systems -- First applications -- Schubert decompositions for type Dn -- Proof of Theorem 4.1.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Cluster algebras.=| ^A1239665;

650 0 a| Grassmann manifolds.=| ^A97834;

650 0 a| Dynkin diagrams.=| ^A323814;

650 0 a| Euler characteristic.=| ^A758100;

650 0 a| Schubert varieties.=| ^A407236;

650 0 a| Affine algebraic groups.=| ^A597019;

650 0 a| Geometry, Algebraic.=| ^A42380;

650 7 a| Commutative algebra -- Arithmetic rings and other special rings -- Cluster algebras.2| msc;

650 7 a| Algebraic geometry -- (Co)homology theory [See also 13Dxx] -- Topological properties.2| msc;

650 7 a| Algebraic geometry -- Special varieties -- Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35].2| msc;

650 7 a| Algebraic geometry -- Projective and enumerative geometry [See also 51-XX] -- Classical problems, Schubert calculus.2| msc;

650 7 a| Associative rings and algebras {For the commutative case, see 13-XX} -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets.2| msc;

650 7 a| Combinatorics {For finite fields, see 11Txx} -- Algebraic combinatorics -- Combinatorial aspects of representation theory [See also 20C30].2| msc;

650 7 a| Algebraic geometry -- Special varieties -- Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15].2| msc;

650 7 a| Associative rings and algebras {For the commutative case, see 13-XX} -- Representation theory of rings and algebras -- Representation type (finite, tame, wild, etc.).2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Weist, Thorsten.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=5990837;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5654277-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/21/2021x| EBOOKz| JERESOURCE;

Quiver grassmannians of extended Dynkin type D part I : Schubert systems and decompositions into affine spaces / Oliver Lorscheid, Thorsten Weist.

Author/creator	Lorscheid, Oliver
Other author	Weist, Thorsten.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2019.
Description	v, 78 pages : illustrations ; 25 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Cluster algebras. Grassmann manifolds. Dynkin diagrams. Euler characteristic. Schubert varieties. Affine algebraic groups. Geometry, Algebraic.

Portion of title	Schubert systems and decompositions into affine spaces
Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1258
Contents	Background -- Schubert systems -- First applications -- Schubert decompositions for type Dn -- Proof of Theorem 4.1.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 77-78).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2020023140
ISBN	9781470436476 (paperback)
ISBN	(ebook)

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Quiver grassmannians of extended Dynkin type D part I : Schubert systems and decompositions into affine spaces / Oliver Lorscheid, Thorsten Weist.

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