相关论文: Decomposability of minimal defect branched coverin…
In this work we study the decomposability property of branched coverings of degree $d$ odd, over the projective plane, where the covering surface has Euler characteristic $\leq 0$. The latter condition is equivalent to say that the defect…
In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.
Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a…
We argue that for a smooth surface S, considered as a ramified cover over the projective plane branched over a nodal-cuspidal curve B one could use the structure of the fundamental group of the complement of the branch curve to understand…
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…
In this paper, we give a complete description of the deformation classes of real structures on minimal ruled surfaces. In particular, we show that these classes are determined by the topology of the real structure, which means that real…
Minimal surfaces in a Riemannian manifold $M^n$ are surfaces which are stationary for area: the first variation of area vanishes. In this paper we focus on surfaces of the topological type of the real projective plane $\R P^2$. We show that…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
There are examples of branched surfaces that do not fully carry laminations, but their preimage in a finite cover does fully carry a lamination
Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we…
We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.
In this paper we study the degeneration of convex real projective structures on bordered surfaces.
In this note we construct examples of covers of the projective line in positive characteristic such that every specialization is inseparable. The result illustrates that it is not possible to construct all covers of the generic r-pointed…
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any m(k)-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k…
Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible)…
We study two decomposition problems in combinatorial geometry. The first part deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in n+1 dimensional complex projective space. We prove that for n is greater than or equal to 5, the Galois covers of any surfaces of…
In this paper we study the homeomorphisms of the disk that are liftable with respect to a simple branched covering. Since any such homeomorphism maps the branch set of the covering onto itself and liftability is invariant up to isotopy…
We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset.