# 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} }

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

#### 11 Citations

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Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds

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For a Calabi-Yau 4-fold $(X,\omega)$, where $X$ is quasi-projective and $\omega$ is a nowhere vanishing section of its canonical bundle $K_X$, the (derived) moduli stack of compactly supported… Expand

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For oriented −1-shifted symplectic derived Artin stacks, Ben-Bassat– Brav–Bussi–Joyce introduced certain perverse sheaves on them which can be regarded as sheaf theoretic categorifications of the… Expand

3-d Calabi--Yau categories for Teichm\"uller theory

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For g, n ≥ 0 a 3-dimensional Calabi-Yau A∞-category Cg,n is constructed such that a component of the space of Bridgeland stability conditions, Stab(Cg,n), is a moduli space of quadratic differentials… Expand

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Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr̀ı-Toda, such as the quintic 3-fold. We express Joyce’s generalised DT invariants counting Gieseker semistable… Expand

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We develop a new method to construct the virtual fundamental classes for quasi-smooth derived schemes using the perverse sheaves of vanishing cycles on their −1-shifted contangent spaces. It is based… Expand

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