Finite morphisms to projective space and capacity theory

The Space of Morphisms on Projective Space

The theory of moduli of morphisms on P generalizes the study of rational maps on P1. This paper proves three results about the space of morphisms on P of degree d > 1, and its quotient by the conjugation action of PGL(n + 1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverma...

Higher Order Singularities of Morphisms to Projective Space

This paper proves existence theorems for higher order singularities of a finite morphism to P"' and deduces a result on simple connectivity of varieties admitting a finite morphism of bounded singularity. The singularities are obtained by successive degeneration of double points of /. Our main tool is R. Schwarzenberger's notion of generalized secant sheaves and the connectedness theorem obtain...

Section 2.7 - Projective Morphisms

Let A be a fixed ring, and consider the projective space PA = ProjA[x0, . . . , xn] over A. On PA we have the invertible sheaf O(1), and the homogenous coordinates x0, . . . , xn give rise to global sections ẋ0, . . . , ẋn ∈ Γ(PA,O(1)). Throughout this section we drop the dot in this notation and just write xi for the global section of O(1). One sees easily that the sheaf O(1) is generated by t...

Homology of Projective Space over Finite Fields

Almost Complex Projective Structures and Their Morphisms

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of...