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In this article we give a condition, which holds in a very general setting, to smooth a rope, of any dimension, embedded in projective space. As a consequence of this we prove that canonically embedded carpets satisfying mild geometric condition[...]texto impreso
Gallego Rodrigo, Francisco Javier ; González, Miguel ; Purnaprajna, Bangere P. | Academic Press | 2013-01his article delves into the relation between the deformation theory of finite morphisms to projective space and the existence of ropes, embedded in projective space, with certain invariants. We focus on the case of canonical double covers X of a[...]texto impreso
Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. | The Academy of Science of the Royal Society of Canada | 2004Le but de cet article est de décrire la classification obtenue dans [GP1] des revêtements galoisiens de degré 4 des surfaces de degré minimal qui sont définis par le morphisme canonique. Cette classification montre que ces revêtements sont ou bi[...]texto impreso
Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. | American Mathematical Society | 2008-10In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double, then they are all fiber produc[...]texto impreso
In this article we classify quadruple Galois canonical covers ? of singular surfaces of minimal degree. This complements the work done in [F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/[...]texto impreso
Gallego Rodrigo, Francisco Javier ; González Andrés, Miguel ; Purnaprajna, Bangere P. | Springer-Verlag | 2010-06-05In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map ca[...]texto impreso
Gallego Rodrigo, Francisco Javier ; González Andrés, Miguel ; Purnaprajna, Bangere P. | Cambridge University Press | 2008-03-14In this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, [...]texto impreso
Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. | American Mathematical Society | 1997-06A K3 carpet S is a double structure on a rational normal scroll such that its dualizing sheaf is trivial and h1(OS) = 0. In this note the authors show that every K3 carpet S can be smoothed, i.e. there exists a flat family over a smooth curve w[...]texto impreso
Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. ; González Andrés, Miguel | Elsevier Science B.V. (North-Holland) | 2008-05Let Y be a smooth Enriques surface. A K3 carpet on Y is a double structure on Y with the same invariants as a smooth K3 surface (i.e., regular and with trivial canonical sheaf). The surface Y possesses an etale K3 double cover X -> (pi) over bar[...]texto impreso
From the introduction: Let X be an irreducible projective variety and L a very ample lLine bundle on X, whose complete linear series defines 'L : X ! P(H0(L)). Let S = 1 m=0 SmH0(X,L) and let R(L) = L1 n=0 H0(X,L n) be the homogeneous coordinate[...]texto impreso
Gallego Rodrigo, Francisco Javier ; Purnaprajna, Bangere P. | American Mathematical Society | 2011-03-07I In this article we study the bicanonical map ?2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ?2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surface[...]texto impreso
In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces. From more general results we, obtain in pa[...]texto impreso
In this article we show that a wide range of multiple structures on curves arise whenever a family of embeddings degenerates to a morphism of degree . One could expect to see, when an embedding degenerates to such a morphism, the appearance of a[...]texto impreso
In this article we present a new technique to handle the study of homogeneous rings of a projective variety endowed with a finite or a generically finite morphism to another variety Y whose geometry is easier to handle. Under these circumstances[...]texto impreso
The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle L on X, we give an optimal numerical criterion[...]
