scholarly journals Limit linear series and ranks of multiplication maps

2020 ◽  
Vol 374 (1) ◽  
pp. 367-405
Author(s):  
Fu Liu ◽  
Brian Osserman ◽  
Montserrat Teixidor i Bigas ◽  
Naizhen Zhang
Keyword(s):  
Linear Series ◽  
Limit Linear Series

scholarly journals Linked determinantal loci and limit linear series

2015 ◽  
Vol 144 (6) ◽  
pp. 2399-2410 ◽  
Author(s):  
John Murray ◽  
Brian Osserman
Keyword(s):  
Linear Series ◽  
Limit Linear Series

scholarly journals Universal limit linear series and descent of moduli spaces

2018 ◽  
Vol 159 (1-2) ◽  
pp. 13-38 ◽  
Author(s):  
Max Lieblich ◽  
Brian Osserman
Keyword(s):  
Moduli Spaces ◽  
Linear Series ◽  
Limit Linear Series

Limit linear series: Basic theory

1986 ◽  
Vol 85 (2) ◽  
pp. 337-371 ◽  
Author(s):  
David Eisenbud ◽  
Joe Harris
Keyword(s):  
Linear Series ◽  
Basic Theory ◽  
Limit Linear Series

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

2018 ◽  
Vol 70 (3) ◽  
pp. 628-682 ◽  
Author(s):  
Ye Luo ◽  
Madhusudan Manjunath
Keyword(s):  
Algebraic Curves ◽  
Linear Series ◽  
Compact Type ◽  
Nodal Curves ◽  
Dual Graphs ◽  
Rank One ◽  
Limit Linear Series

AbstractWe investigate the smoothing problem of limit linear series of rank one on an enrichment of the notions of nodal curves and metrized complexes called saturated metrized complexes. We give a finitely verifiable full criterion for smoothability of a limit linear series of rank one on saturated metrized complexes, characterize the space of all such smoothings, and extend the criterion to metrized complexes. As applications, we prove that all limit linear series of rank one are smoothable on saturated metrized complexes corresponding to curves of compact-type, and 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. In addition, we give a full combinatorial criterion for smoothable limit linear series of rank one on saturated metrized complexes corresponding to nodal curves whose dual graphs are made of separate loops.

scholarly journals Connectedness of Brill–Noether Loci via Degenerations

2018 ◽  
Vol 2019 (19) ◽  
pp. 6162-6178 ◽  
Author(s):  
Brian Osserman
Keyword(s):  
Linear Series ◽  
Positive Dimension ◽  
Recent Advances ◽  
Limit Linear Series

Abstract We show that limit linear series spaces for chains of curves are reduced. Using recent advances in the foundations of limit linear series, we then use degenerations to study the question of connectedness for spaces of linear series with imposed ramification at up to two points. We find that in general, these spaces may not be connected even when they have positive dimension, but we prove a criterion for connectedness which generalizes the theorem previously proved by Fulton and Lazarsfeld in the case without imposed ramification.

scholarly journals Abel maps and limit linear series

2013 ◽  
Vol 62 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Eduardo Esteves ◽  
Brian Osserman
Keyword(s):  
Linear Series ◽  
Limit Linear Series

scholarly journals Limit linear series for vector bundles

2014 ◽  
Vol 66 (4) ◽  
pp. 555-562 ◽  
Author(s):  
Montserrat Teixidor i Bigas
Keyword(s):  
Vector Bundles ◽  
Linear Series ◽  
Limit Linear Series
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