Abel Maps and Limit Linear Series for Curves of Compact Type with Three Irreducible Components

2018 ◽  
Vol 49 (3) ◽  
pp. 549-575
Author(s):  
Gabriel Muñoz
Keyword(s):  
Linear Series ◽  
Compact Type ◽  
Irreducible Components ◽  
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 Limit linear series for curves not of compact type

2019 ◽  
Vol 2019 (753) ◽  
pp. 57-88 ◽  
Author(s):  
Brian Osserman
Keyword(s):  
Moduli Space ◽  
Linear Series ◽  
Restricted Class ◽  
Compact Type ◽  
Nodal Curves ◽  
Equivalent Definition ◽  
Two Component ◽  
Limit Linear Series ◽  
Definition Of

AbstractWe introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding specialization result. For a more restricted class of curves which simultaneously generalizes two-component curves and curves of compact type, we give an equivalent definition of limit linear series, which is visibly a generalization of the Eisenbud–Harris definition. Finally, for the same class of curves, we prove a smoothing theorem which constitutes an improvement over known results even in the compact-type case.

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 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.

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