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- Title
UNWEIGHTED DONALDSON–THOMAS THEORY OF THE BANANA 3-FOLD WITH SECTION CLASSES.
- Authors
Leigh, Oliver
- Abstract
We further the study of the Donaldson–Thomas theory of the banana 3-folds which were recently discovered and studied by Bryan [ 3 ]. These are smooth proper Calabi–Yau 3-folds which are fibred by Abelian surfaces such that the singular locus of a singular fibre is a non-normal toric curve known as a 'banana configuration'. In [ 3 ], the Donaldson–Thomas partition function for the rank 3 sub-lattice generated by the banana configurations is calculated. In this article, we provide calculations with a view towards the rank 4 sub-lattice generated by a section and the banana configurations. We relate the findings to the Pandharipande–Thomas theory for a rational elliptic surface and present new Gopakumar–Vafa invariants for the banana 3-fold.
- Subjects
BANANAS; PARTITION functions
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p867
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa007