Image stitching algorithms often adopt the global transformation, such as homography, and work well for planar scenes or parallax free camera motions. However, these conditions are easily violated in practice. With casual camera motions, variable taken views, large depth change, or complex structures, it is a challenging task for stitching these images. The global transformation model often pro...

And there are similar disjoint decompositions starting with the (x, z)-plane or the (y, z)-plane. When K = R, our intuition is that the real projective line PR is an ordinary line with a point at infinity identifying its opposite directions, and the projective plane is an ordinary plane surrounded by a circle at infinity identifying its opposite directions. The real projective plane differs fro...

An embedding of a point-line geometry Γ is usually defined as an injective mapping ε from the point-set of Γ to the set of points of a projective space such that ε(l) is a projective line for every line l of Γ. However, different situations are considered in the literature, where ε(l) is allowed to be a subline of a projective line or a curve. In this paper we propose a more general definition ...

Exact bounds for the positions of the branch points for cyclic coverings of the p-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato’s ∗-trees, and secondly by giving explicit matrix representations of the Schottky groups corresponding to the Mumford curves above the projective line through combinatorial group theory.

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weighted Weak Factorization Theorems of nonsingular projective varieties and more generally projective varieties with finite quotient singularities. Along the way, we will also mention some progresses on birational geom...

We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli R that can not be defined over R is also given.

Let A and B be very ample line bundles on a projective toric variety. Then, it is proved that the multiplication map Γ(A)⊗ Γ(B) → Γ(A⊗B) of global sections of the two bundles is surjective. As a consequence, it is showed that any very ample line bundle on a projective toric variety is normally generated. As an application we show that any ample line bundle on a toric Calabi-Yau hypersurface is ...

In this paper, we provide some exact formulas for the projective dimension and regularity of powers edge ideals vertex-weighted rooted forests. These are functions weight vertices number edges.

let $mathcal{x}$ be a class of $r$-modules‎. ‎in this paper‎, ‎we investigate ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective (projective) complexes which are generalizations of injective (projective) and dg-injecti‎‎ve (projective) complexes‎. ‎we prove that some known results can be extended to the class of ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective ...

We consider blowups at a general point of weighted projective planes and, more generally, toric surfaces with Picard number one. give unifying construction negative curves on these such that all previously known families appear as boundary cases this. The classification consists two classes said curves, each depending parameters. Every curve in is algebraically related to other both classes; th...