Barbieri, A., Stoppa, J. and Sutherland, T. (2019) A construction of Frobenius manifolds from stability conditions. Proceedings of the London Mathematical Society, 118 (6). pp. 1328-1366. ISSN 0024-6115
Abstract
© 2018 London Mathematical Society A finite quiver Q without loops or 2-cycles defines a CY3 triangulated category D(Q) and a finite heart A(Q)⊂D(Q). We show that if Q satisfies some (strong) conditions, then the space of stability conditions (A(Q))) supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in D(Q). In the case of An evaluating the family at a special point, we recover a branch of the Saito Frobenius structure of the An singularity y2=xn+1. We give examples where applying the construction to each mutation of Q and evaluating the families at a special point yields a different branch of the maximal analytic continuation of the same semisimple Frobenius manifold. In particular, we check that this holds in the case of An, n5.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 London Mathematical Society. This is an author-produced version of a paper subsequently published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 May 2019 14:13 |
Last Modified: | 04 Jun 2019 11:53 |
Status: | Published |
Publisher: | London Mathematical Society |
Refereed: | Yes |
Identification Number: | 10.1112/plms.12217 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:146664 |