Abstract The aim of this article is to study the geometry Bott-Chern hypercohomology from bimeromorphic point view. We construct some new invariants involving cohomology for sheaf germs pluriharmonic functions, truncated holomorphic de Rham cohomology, and cohomology. To define these invariants, by using a sheaf-theoretic approach, we establish blow-up formula together with canonical morphism h...

In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, prove that given two X and $$X'$$ , following conditions are equivalent: As a consequence, affirmatively answer cohomological rigidity problem for manifolds.

In type A, Bott-Samelson varieties are posets in which ascending chains are flags of vector spaces. They come equipped with a map into the flag variety G/B. These varieties are mostly studied in the case in which the map into G/B is birational to the image. In this paper we study Bott-Samelsons for general types, more precisely, we study the combinatorics a fiber of the map into G/B when it is ...

The talk consists of four parts. In the first part, the motivation is explained for revisiting certain questions in circuit theory, in particular, the synthesis theory of “one-port” (i.e. with a pair of external driving terminals) RLC networks and the questions of minimality associated with the Bott-Duffin procedure. The motivation relates to the synthesis of passive mechanical impedances and t...