Smoothable locally non Cohen-Macaulay multiple structures on curves



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Gallego Rodrigo, Francisco Javier and González, Miguel and Purnaprajna, Bangere P. (2014) Smoothable locally non Cohen-Macaulay multiple structures on curves. Collectanea Mathematica, 65 (3). pp. 417-433. ISSN 0010-0757

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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.

Item Type:Article
Uncontrolled Keywords:Deformation of morphisms; Multiple structures; Double structures; Locally non Cohen-Macaulay schemes; Degenerations of curves
Subjects:Sciences > Mathematics > Algebra
ID Code:26871
Deposited On:30 Sep 2014 10:42
Last Modified:30 Sep 2014 10:42

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