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.

In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formula between the relative Chern character of the Bott morphism and the relative Thom form.

We give explicit harmonic representatives of Dolbeault cohomology Oeljeklaus-Toma manifolds and show that they are geometrically formal. also Bott-Chern type $(s,1)$ study the Angella-Tomassini inequality.