extension spaces
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2020 ◽  
pp. 1-44
Author(s):  
İlke Çanakçı ◽  
David Pauksztello ◽  
Sibylle Schroll

Abstract We give a complete description of a basis of the extension spaces between indecomposable string and quasi-simple band modules in the module category of a gentle algebra.



2019 ◽  
Vol 62 (1) ◽  
pp. 147-182 ◽  
Author(s):  
ALEXANDER GARVER ◽  
THOMAS MCCONVILLE

AbstractThe purpose of this paper is to understand lattices of certain subcategories in module categories of representation-finite gentle algebras called tiling algebras, as introduced by Coelho Simões and Parsons. We present combinatorial models for torsion pairs and wide subcategories in the module category of tiling algebras. Our models use the oriented flip graphs and noncrossing tree partitions, previously introduced by the authors, and a description of the extension spaces between indecomposable modules over tiling algebras. In addition, we classify two-term simple-minded collections in bounded derived categories of tiling algebras. As a consequence, we obtain a characterization of c-matrices for any quiver mutation-equivalent to a type A Dynkin quiver.



2014 ◽  
Vol 25 (05) ◽  
pp. 1450047 ◽  
Author(s):  
Insong Choe ◽  
G. H. Hitching

A symplectic or orthogonal bundle V of rank 2n over a curve has an invariant t(V) which measures the maximal degree of its isotropic subbundles of rank n. This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles. We study this stratification by relating it to another one given by secant varieties in certain extension spaces. We give a sharp upper bound on t(V), which generalizes the classical Nagata bound for ruled surfaces and the Hirschowitz bound for vector bundles, and study the structure of the stratifications on the moduli spaces. In particular, we compute the dimension of each stratum. We give a geometric interpretation of the number of maximal Lagrangian subbundles of a general symplectic bundle, when this is finite. We also observe some interesting features of orthogonal bundles which do not arise for symplectic bundles, essentially due to the richer topological structure of the moduli space in the orthogonal case.





2005 ◽  
Vol 115 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Jong Kyu Kim ◽  
Donal O’Regan


1993 ◽  
Vol 10 (1) ◽  
pp. 23-45 ◽  
Author(s):  
Bernd Sturmfels ◽  
Günter M. Ziegler


1992 ◽  
Vol 42 (3) ◽  
pp. 501-515
Author(s):  
Le Mau Hai ◽  
Nguyen Van Khue
Keyword(s):  






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