On jumping lines of vector bundles on $$\mathbb {P}^n$$ P n

Commutativity degree of $mathbb{Z}_p$≀$mathbb{Z}_{p^n}

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

Construction of Low Rank Vector Bundles on P and P

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P5. In characteristic p, we obtain rank two bundles on P4 and rank three bundles on P5. In arbitrary characteristic, we obtain rank three bundles on P4 and rank two bundles on the quadric S5 in P6.

On nonlocal elliptic system of $p$-Kirchhoff-type in $mathbb{R}^N$

‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.

Arrangements of Hyperplanes and Vector Bundles on P

Vector Bundles on Products of Varieties with n-blocks Collections

Here we consider the product of varieties with n-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson’s type spectral sequences generalized by Costa and Miró-Roig. Moreover we introduce a notion of CastelnuovoMumford regularity on a product of finitely many projectiv...