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On kernel bundles over reducible curves with a node
International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-06-23 , DOI: 10.1142/s0129167x20500548
Sonia Brivio; Filippo F. Favale

Given a vector bundle E on a complex reduced curve C and a subspace V of H0(E) which generates E, one can consider the kernel of the evaluation map evV:V𝒪CE, i.e. the kernel bundleME,V associated to the pair (E,V). Motivated by a well-known conjecture of Butler about the semistability of ME,V and by the results obtained by several authors when the ambient space is a smooth curve, we investigate the case of a reducible curve with one node. Unexpectedly, we are able to prove results which goes in the opposite direction with respect to what is known in the smooth case. For example, ME,H0(E) is actually quite never w-semistable. Conditions which gives the w-semistability of ME,V when VH0(E) or when E is a line bundle are then given.

更新日期:2020-08-08

 

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