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arXiv · 1603.00972

Donaldson-Thomas Transformation of Grassmannian

Daping Weng
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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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Daping Weng. 2016-03-03. Donaldson-Thomas Transformation of Grassmannian. https://arxiv.org/abs/1603.00972

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