Donaldson-Thomas Transformation of Grassmannian

Abstract

Kontsevich and Soibelman defined the notion of Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. A family of examples of such categories can be constructed from an arbitrary cluster variety. The corresponding Donaldson-Thomas invariants are encoded by a special formal automorphism of the cluster variety, known as Donaldson-Thomas transformation. Fix two integers $m$ and $n$ with $1<m<m+1<n$. It is known that the configuration space ${\mathrm{Conf}}_n({\mathbb{P}}^{m-1})$, closely related to Grassmannian ${\mathrm{Gr}}_m(n)$, is a cluster Poisson variety. In this paper we determine the Donaldson-Thomas transformation of ${\mathrm{Conf}}_n({\mathbb{P}}^{m-1})$ as an explicitly defined birational automorphism of ${\mathrm{Conf}}_n({\mathbb{P}}^{m-1})$. Its variant acts on the Grassmannian by a birational automorphism.

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Cited by in corpus (7)

• Cyclic Sieving and Cluster Duality of Grassmannian
• A survey on maximal green sequences
• Moment curves and cyclic symmetry for positive Grassmannians
• Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups
• Cluster Structures on Double Bott-Samelson Cells
• Positive Braid Links with Infinitely Many Fillings
• Donaldson-Thomas Transformation of Double Bruhat Cells in General Linear Groups