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Relative Calabi–Yau structures II: shifted Lagrangians in the moduli of objects
Selecta Mathematica ( IF 1.2 ) Pub Date : 2021-07-01 , DOI: 10.1007/s00029-021-00642-5
Christopher Brav , Tobias Dyckerhoff

We show that a Calabi–Yau structure of dimension d on a smooth dg category \({C}\) induces a symplectic form of degree \(2-d\) on ‘the moduli space of objects’ \({{\mathcal {M}}}_{{C}}\). We show moreover that a relative Calabi–Yau structure on a dg functor \({C}\rightarrow { D}\) compatible with the absolute Calabi–Yau structure on C induces a Lagrangian structure on the corresponding map of moduli \({{\mathcal {M}}}_{{ D}} \rightarrow {{\mathcal {M}}}_{{C}}\).



中文翻译:

相对 Calabi-Yau 结构 II:物体模量中的移动拉格朗日

我们表明,尺寸的卡拉比-丘结构d在光滑DG类别\({C} \)诱导程度的辛形式\(2- d \)上“的对象的模空间” \({{\ mathcal {M}}}_{{C}}\) . 我们而且表明,在分克函子的相对卡拉比-丘结构\({C} \ RIGHTARROW {d} \)与绝对卡拉比-丘结构兼容Ç诱导的对应地图上的拉格朗日结构模量\({{ \mathcal {M}}}_{{ D}} \rightarrow {{\mathcal {M}}}_{{C}}\)

更新日期:2021-07-01
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