In this paper we deal with polarizations on a nodal curve C with smooth components. Our aim is to study and characterize a class of polarizations, which we call “good”, for which depth one sheaves on C reflect some properties that hold for vector bundles on smooth curves. We will concentrate, in particular, on the relation between the w̲-stability of OC and the goodness of w̲. We prove that these two concepts agree when C is of compact type and we conjecture that the same should hold for all nodal curves.
Brivio, S., Favale, F. (2021). Nodal curves and polarizations with good properties. REVISTA MATEMATICA COMPLUTENSE [10.1007/s13163-021-00404-z].
Nodal curves and polarizations with good properties
Brivio, S;Favale, F
2021
Abstract
In this paper we deal with polarizations on a nodal curve C with smooth components. Our aim is to study and characterize a class of polarizations, which we call “good”, for which depth one sheaves on C reflect some properties that hold for vector bundles on smooth curves. We will concentrate, in particular, on the relation between the w̲-stability of OC and the goodness of w̲. We prove that these two concepts agree when C is of compact type and we conjecture that the same should hold for all nodal curves.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.