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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of syzygy bundles


Authors: Pedro Macias Marques and Rosa María Miró-Roig
Journal: Proc. Amer. Math. Soc. 139 (2011), 3155-3170
MSC (2010): Primary 14J60, 14F05
Published electronically: January 28, 2011
MathSciNet review: 2811270
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Abstract: We show that given integers $ N$, $ d$ and $ n$ such that $ {N\ge2}, (N,d,n)$ $ \ne(2,2,5)$, and $ {N+1\le n\le\tbinom{d+N}{N}}$, there is a family of $ n$ monomials in $ K\left[X_0,\ldots,X_N\right]$ of degree $ d$ such that their syzygy bundle is stable. Case $ {N\ge3}$ was obtained independently by Coanda with a different choice of families of monomials.

For $ {(N,d,n)=(2,2,5)}$, there are $ 5$ monomials of degree $ 2$ in $ K\left[X_0,X_1,X_2\right]$ such that their syzygy bundle is semistable.


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Additional Information

Pedro Macias Marques
Affiliation: Departamento de Matemática, Universidade de Évora, Rua Romão Ramalho, 59, 7000–671 Évora, Portugal
Address at time of publication: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
Email: pmm@uevora.pt

Rosa María Miró-Roig
Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
Email: miro@ub.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10745-7
PII: S 0002-9939(2011)10745-7
Keywords: Stability, vector bundles
Received by editor(s): November 25, 2009
Received by editor(s) in revised form: August 17, 2010
Published electronically: January 28, 2011
Additional Notes: The first author was partially supported by Fundação para a Ciência e a Tecnologia, under grant SFRH/BD/27929/2006, and by CIMA – Centro de Investigação em Matemática e Aplicações, Universidade de Évora.
The second author was partially supported by MTM2007-61104.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society