Strong positivity for quantum theta bases of quantum cluster algebras
B Davison, T Mandel - Inventiones mathematicae, 2021 - Springer
We construct “quantum theta bases,” extending the set of quantum cluster monomials, for
various versions of skew-symmetric quantum cluster algebras. These bases consist …
various versions of skew-symmetric quantum cluster algebras. These bases consist …
Theta bases and log Gromov-Witten invariants of cluster varieties
T Mandel - Transactions of the American Mathematical Society, 2021 - ams.org
Using heuristics from mirror symmetry, combinations of Gross, Hacking, Keel, Kontsevich,
and Siebert have given combinatorial constructions of canonical bases of “theta functions” …
and Siebert have given combinatorial constructions of canonical bases of “theta functions” …
Newton–Okounkov bodies and minimal models for cluster varieties
L Bossinger, MW Cheung, T Magee… - Advances in Mathematics, 2024 - Elsevier
Let Y be a (partial) minimal model of a scheme V with a cluster structure (of type A, X or of a
quotient of A or a fibre of X). Under natural assumptions, for every choice of seed we …
quotient of A or a fibre of X). Under natural assumptions, for every choice of seed we …
Theta Function Basis of the Cox ring of Postive 2d Looijenga pairs
S Keel, L White - arXiv preprint arXiv:2412.01774, 2024 - arxiv.org
We give a canonical basis of theta functions for the Cox ring of two dimensional Looijenga
pairs with affine interior, with structure constants naive counts of k-analytic disks in the total …
pairs with affine interior, with structure constants naive counts of k-analytic disks in the total …
Classification of rank 2 cluster varieties
T Mandel - SIGMA. Symmetry, Integrability and Geometry: Methods …, 2019 - emis.de
We classify rank $2 $ cluster varieties (those for which the span of the rows of the exchange
matrix is $2 $-dimensional) according to the deformation type of a generic fiber $ U $ of their …
matrix is $2 $-dimensional) according to the deformation type of a generic fiber $ U $ of their …
Cluster structures on Cox rings
L Francone - arXiv preprint arXiv:2412.04173, 2024 - arxiv.org
We construct a graded cluster algebra structure on the Cox ring of a smooth complex variety
$ Z $, depending on a base cluster structure on the ring of regular functions of an open …
$ Z $, depending on a base cluster structure on the ring of regular functions of an open …