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...

Bott-Samelson varieties factor the flag variety G/B into a product of CP’s with a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to tran...

Expansion of a polyglutamine-encoding trinucleotide CAG repeat in the androgen receptor (AR) gene causes spinal and bulbar muscular atrophy (SBMA, or Kennedy’s disease). SBMA is an adult-onset disease characterized by progressive muscle weakness and atrophy due to the degeneration of lower motor neurons in the brainstem and spinal cord. At present, effective disease-modifying treatment is not a...

A subcomplex of a residual complex on projective space is constructed for computing the cohomology modules of locally free sheaves. A constructive new proof of the Bott formula is given by explicitly exhibiting bases for the cohomology modules.

We study Bott-Samelson varieties for the group GLn(C), their toric degenerations and standard monomial type bases for their homogeneous coordinate rings. A 3-dimensional example is described in detail.

In [AB], Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly nonorientable surfaces.