RT Journal Article
T1 Smoothable locally non Cohen-Macaulay multiple structures on curves
A1 Gallego Rodrigo, Francisco Javier
A1 González, Miguel
A1 Purnaprajna, Bangere P.
AB 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 locally Cohen-Macaulay multiple structure of certain kind (a so-called rope of multiplicity ). We show that this expectation is naive and that locally non Cohen-Macaulay multiple structures also occur in this situation. In seeing this we find out that many multiple structures can be smoothed. When we specialize to the case of double structures we are able to say much more. In particular, we find numerical conditions, in terms of the degree and the arithmetic genus, for the existence of many locally Cohen-Macaulay and non Cohen-Macaulay smoothable double structures. Also, we show that the existence of these double structures is determined, although not uniquely, by the elements of certain space of vector bundle homomorphisms, which are related to the first order infinitesimal deformations of . In many instances, we show that, in order to determine a double structure uniquely, looking merely at a first order deformation of is not enough; one needs to choose also a formal deformation.
PB Springer
SN 0010-0757
YR 2014
FD 2014-09
LK https://hdl.handle.net/20.500.14352/33651
UL https://hdl.handle.net/20.500.14352/33651
LA eng
NO UCM
NO Simons Foundation
NO NSF
DS Docta Complutense
RD 19 abr 2025