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摘要翻译：
本文从阿贝尔范畴及其导出范畴的观点出发，研究了射影簇的形式圆盘上形式形变的一般纤维。一般纤维相干束的阿贝尔范畴由形式变形直接构造，并证明其在Laurent级数域上是线性的。对一般纤维的衍生类别的各种候选进行了比较。如果该簇是一个具有平凡正则丛的曲面，我们证明了一般纤维的导出范畴又是一个具有Serre函子的线性三角范畴，其Serre函子由移位函子的平方给出。
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英文标题：
《Formal deformations and their categorical general fibre》
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作者：
Daniel Huybrechts, Emanuele Macri, Paolo Stellari
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Category Theory 范畴理论
分类描述：Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
丰富范畴，topoi，abelian范畴，monoidal范畴，同调代数
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英文摘要：
We study the general fibre of a formal deformation over the formal disk of a projective variety from the view point of abelian and derived categories. The abelian category of coherent sheaves of the general fibre is constructed directly from the formal deformation and is shown to be linear over the field of Laurent series. The various candidates for the derived category of the general fibre are compared. If the variety is a surface with trivial canonical bundle, we show that the derived category of the general fibre is again a linear triangulated category with a Serre functor given by the square of the shift functor.
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PDF链接：
https://arxiv.org/pdf/0809.3201
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