# Orientation data for moduli spaces of coherent sheaves over Calabi–Yau 3-folds

@article{Joyce2020OrientationDF,
title={Orientation data for moduli spaces of coherent sheaves over Calabi–Yau 3-folds},
author={Dominic Joyce and Markus Upmeier},
journal={arXiv: Algebraic Geometry},
year={2020}
}
• Published 1 January 2020
• Mathematics
• arXiv: Algebraic Geometry
Let $X$ be a compact Calabi-Yau 3-fold, and write $\mathcal M,\bar{\mathcal M}$ for the moduli stacks of objects in coh$(X),D^b$coh$(X)$. There are natural line bundles $K_{\mathcal M}\to\mathcal M$, $K_{\bar{\mathcal M}}\to\bar{\mathcal M}$, analogues of canonical bundles. Orientation data on $\mathcal M,\bar{\mathcal M}$ is an isomorphism class of square root line bundles $K_{\mathcal M}^{1/2},K_{\bar{\mathcal M}}^{1/2}$, satisfying a compatibility condition on the stack of short exact… Expand
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