We initiate and develop a framework to handle the specialisation morphism as a filtered morphism for the perverse, and for the perverse Leray filtration, on the cohomology with constructible coefficients of varieties and morphisms parameterised by a curve. As an application, we use this framework to carry out a detailed study of filtered specialisation for the Hitchin morphisms associated with the compactification of Dolbeault moduli spaces in [de 2018].

中文翻译：

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Perverse Leray 过滤和专门化与 Hitchin 态射的应用

我们启动并开发了一个框架来处理专门化态射作为反常的过滤态射，以及对于反常 Leray 过滤，在具有可构造系数的上同调和由曲线参数化的态射。作为一个应用程序，我们使用该框架对 [de 2018] 中与 Dolbeault 模空间紧致化相关的 Hitchin 态射的过滤特化进行了详细研究。