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In his work on deformation quantization of algebraic varieties Kontsevich introduced the notion of algebroid as a certain generalization of a sheaf of algebras. We construct algebroids which are given locally by NC-smooth thickenings in the sense of Kapranov, over two classes of smooth varieties: the bases of miniversal families of vector bundles on projective curves, and the bases of miniversal families of quiver representations.
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Combinatorics of exceptional sequences in type A
Exceptional sequences are certain sequences of quiver representations. We introduce a class of objects called strand diagrams and use these to classify exceptional sequences of representations of a quiver whose underlying graph is a type An Dynkin diagram. We also use variations of these objects to classify $$c$$-matrices of such quivers, to interpret exceptional sequences as linear extensions of explicitly constructed posets, and to give a simple bijection between exceptional sequences and certain saturated chains in the lattice of noncrossing partitions.
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- Award ID(s):
- 1638352
- PAR ID:
- 10104978
- Date Published:
- Journal Name:
- The Electronic journal of combinatorics
- Volume:
- 26
- Issue:
- 1
- ISSN:
- 1077-8926
- Page Range / eLocation ID:
- 1-20
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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