Division Theorems and Twisted Complexes

Hypercohomologies of truncated twisted holomorphic de Rham complexes

We investigate the hypercohomologies of truncated twisted holomorphic de Rham complexes on (not necessarily compact) complex manifolds. In particular, we generalize Leray-Hirsch, Künneth and Poincaré-Serre duality theorems on them. At last, a blowup formula is given, which affirmatively answers a question posed by Chen, Y. and Yang, S. in \cite{CY}.

Blow-up formulae for twisted cohomologies with supports

We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of complex blow-up formulae for twisted Dolbeault cohomology on arbitrary complex manifolds and the ones of generalized blow-ups formulae for twisted de Rham cohomology on arbitrary oriented smooth manifolds. These expressions are induced by the morphisms of (simple or double) complexes of spaces of forms and currents rather than just the maps between cohomologies, w…

Division Theorems for the Koszul Complex

We establish a twisted version of Skoda's estimate for the Koszul complex from which we get division theorems for the Koszul complex. This generalizes Skoda's division theorem. We also show how to use Skoda triples to produce division theorems for the Koszul complex.

正加权齐次除子的扭曲对数复形

Twisted logarithmic complexes of positively weighted homogeneous divisors

本文研究正加权齐次除子的扭曲对数复形的拟同构条件，证明LCT与Bernstein-Sato多项式根及一阶算子生成零化子等价，并给出超平面排列情形的简单证明。