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arXiv · 2210.12986

Theta functions and adiabatic curvature on an Abelian variety

Ching-Hao Chang·Jih-Hsin Cheng·I-Hsun Tsai
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Abstract

For an ample line bundle $L$ on an Abelian variety $M$, we study the theta functions associated with the family of line bundles $L\otimes T$ on $M$ indexed by $T\in \text{Pic}^{0}(M)$. Combined with an appropriate differential geometric setting, this leads to an explicit curvature computation of the direct image bundle $E$ on $\text{Pic}^{0}(M)$, whose fiber $E_{T}$ is the vector space spanned by the theta functions for the line bundle $L\otimes T$ on $M$. Some algebro-geometric properties of $E$ are also remarked.

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Ching-Hao Chang, Jih-Hsin Cheng, I-Hsun Tsai. 2022-10-24. Theta functions and adiabatic curvature on an Abelian variety. https://arxiv.org/abs/2210.12986

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