A finite dimensional proof of Verlinde Formula

Xiaotao Sun; Mingshuo Zhou

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arXiv · 2001.11647

A finite dimensional proof of Verlinde Formula

Xiaotao Sun·Mingshuo Zhou

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Abstract

We prove two recurrence relations among dimensions $$D_g(r,d,\omega):={\rm dim}\,{\rm H}^0(\mathcal{U}_{C,\,\omega},\Theta_{\mathcal{U}_{C,\,\omega}})$$ of spaces of generalized theta functions on moduli spaces $\mathcal{U}_{C,\,\omega}$. By using of these recurrence relations, an explicit formula (Verlinde formula) of $D_g(r,d,\omega)$ is proved (See Theorem 4.3).

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Xiaotao Sun, Mingshuo Zhou. 2020-01-31. A finite dimensional proof of Verlinde Formula. https://arxiv.org/abs/2001.11647

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