Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves

Research paper by Ye Luo, Madhusudan Manjunath

Indexed on: 21 Oct '15Published on: 21 Oct '15Published in: Mathematics - Algebraic Geometry


We investigate the smoothing problem of limit linear series of rank one on an enrichment of nodal curves called saturated metrized complexes. Our main result is an effective characterization for smoothability of a limit linear series of rank one. Furthermore, we characterize the space of all possible smoothings. We present two applications of our results: i. We prove that every (refined) limit linear series of rank one on a saturated metrized complex of compact-type is smoothable, corresponding to a theorem for nodal curves due to Eisenbud and Harris. ii. We prove an analogue for saturated metrized complexes of a theorem of Harris and Mumford on the characterization of nodal curves contained in a given gonality stratum.