naa a22 4500 51076066X CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0083-6 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0083-6 An infinitesimal condition to smooth ropes [Elektronische Daten] [Francisco Gallego, Miguel González, Bangere Purnaprajna] 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 conditions can be smoothed. Our condition for smoothing a rope $\widetilde{Y}$ can be stated very transparently in terms of the cohomology class of a suitable first order infinitesimal deformation of a morphism ϕ associated to $\widetilde{Y}$ . In order to prove these results we find a sufficient condition, of independent interest, for a morphism ϕ from a smooth variety X to projective space, finite onto a smooth image, to be deformed to an embedding. Another application of this result on deformation of morphisms is the construction of smooth varieties in projective space with given invariants. We illustrate this by constructing canonically embedded surfaces with $c_{1}^{2}=3p_{g}-7$ and deriving some interesting properties of their moduli spaces. The results of this article bear further evidence to the complexity of the moduli of surfaces of general type and its sharp contrast with the moduli of other objects such as curves or K3 surfaces. Revista Matemática Complutense, 2011 Deformation of morphisms nationallicence Embedding nationallicence Smoothing nationallicence Rope nationallicence Canonical surface nationallicence Gallego Francisco Departamento de Álgebra, Universidad Complutense de Madrid, Madrid, Spain aut González Miguel Departamento de Álgebra, Universidad Complutense de Madrid, Madrid, Spain aut Purnaprajna Bangere Department of Mathematics, University of Kansas, Lawrence, KS, USA aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 253-269 1139-1138 26:1<253 2013 26 13163 https://doi.org/10.1007/s13163-011-0083-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0083-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gallego Francisco Departamento de Álgebra, Universidad Complutense de Madrid, Madrid, Spain aut NATIONALLICENCE 700 1- González Miguel Departamento de Álgebra, Universidad Complutense de Madrid, Madrid, Spain aut NATIONALLICENCE 700 1- Purnaprajna Bangere Department of Mathematics, University of Kansas, Lawrence, KS, USA aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 253-269 1139-1138 26:1<253 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer