It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. Endomorphisms of the projective spaces are also discussed and some results on invariant subvarieties under the pullback of the endomorphism are obt...

We explore the codimension one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex ...

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normalcrossing quasi-projective orbifold groups. Finally, we extend Sakuma’s formula for the first Betti number of abelian cove...

The Macaulayfication of a Noetherian scheme X is a birational proper morphism Y → X such that Y is a CohenMacaulay scheme. Of course, a desingularization is a Macaulayfication and Hironaka gave a desingularization of arbitrary algebraic variety over a field of characteristic 0. In 1978 Faltings gave a Macaulayfication of a quasi-projective scheme whose nonCohen-Macaulay locus is of dimension 0 ...

Naturalness of warping is gaining extensive attention in image stitching. Recent warps such as SPHP, AANAP and GSP, use a global similarity to effectively mitigate projective distortion (which enlarges regions), however, they necessarily bring in perspective distortion (which generates inconsistency). In this paper, we propose a quasi-homography warp, which balances perspective distortion again...

By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS , such that RP is a finitely generated projective generator in R-Mod and S = EndR(P ). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPS . Here we start from the o...

Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique, including the existence of finite quasi-sections in certain projective morphisms, and the existence of hypersurfaces in X/S containing a given closed subsch...

We give a new proof of the Adams-Riemann-Roch theorem for a smooth projective morphism in the situation where the base scheme is of characteristic p > 0 and is regular and quasi-projective over a noetherian affine scheme. We also answer a question of B. Köck.