Introduces the inflation functor from cochain complexes to bicomplexes as part of a Quillen adjunction in pluripotential homological algebra, enabling an infinity-category of bicomplexes.
Autour de la cohomologie de Bott-Chern
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abstract
The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa manifold is investigated as a typical example of what occurs in the non K\"ahler case. Elementary applications to the Kodaira-Spencer deformation theory and to the calculation of Chern classes are given.
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UNVERDICTED 2representative citing papers
Under mild assumptions on the central fiber, the limit of Kähler manifolds under holomorphic deformation is Kähler.
citing papers explorer
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The inflation functor in pluripotential homological algebra
Introduces the inflation functor from cochain complexes to bicomplexes as part of a Quillen adjunction in pluripotential homological algebra, enabling an infinity-category of bicomplexes.
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The limits of Kahler manifolds under holomorphic deformations
Under mild assumptions on the central fiber, the limit of Kähler manifolds under holomorphic deformation is Kähler.