RT Journal Article
T1 An infinitesimal condition to smooth ropes
A1 Gallego Rodrigo, Francisco Javier
A1 González, Miguel
A1 Purnaprajna, Bangere P.
AB 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 can be stated very transparently in terms of the cohomology class of a suitable first order infinitesimal deformation of a morphism I center dot associated to . In order to prove these results we find a sufficient condition, of independent interest, for a morphism I center dot 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 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.
PB Springer
SN 1139-1138
YR 2013
FD 2013-01
LK https://hdl.handle.net/20.500.14352/33255
UL https://hdl.handle.net/20.500.14352/33255
LA eng
NO UCM
NO General Research Fund (GRF) of the University of Kansas
DS Docta Complutense
RD 7 abr 2025