TY - JOUR

T1 - Limit linear series for curves of compact type with three irreducible components

AU - Muñoz, Gabriel

N1 - Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

PY - 2020/10/2

Y1 - 2020/10/2

N2 - Our aim in this work is to study exact Osserman limit linear series on curves of compact type X with three irreducible components. This case is quite different from the case of two irreducible components studied by Osserman. For instance, for curves of compact type with two irreducible components, every refined Eisenbud-Harris limit linear series has a unique exact extension. But, for the case of three irreducible components, this property is no longer true. We find a condition characterizing when a given refined Eisenbud-Harris limit linear series has a unique exact extension. To do this, it is necessary to understand how to construct exact extensions. We find a constructive method, which describes how to construct all exact extensions of refined limit linear series. By our method, we get that every refined limit linear series has at least one exact extension.

AB - Our aim in this work is to study exact Osserman limit linear series on curves of compact type X with three irreducible components. This case is quite different from the case of two irreducible components studied by Osserman. For instance, for curves of compact type with two irreducible components, every refined Eisenbud-Harris limit linear series has a unique exact extension. But, for the case of three irreducible components, this property is no longer true. We find a condition characterizing when a given refined Eisenbud-Harris limit linear series has a unique exact extension. To do this, it is necessary to understand how to construct exact extensions. We find a constructive method, which describes how to construct all exact extensions of refined limit linear series. By our method, we get that every refined limit linear series has at least one exact extension.

KW - Compact type curves

KW - limit linear series

UR - http://www.scopus.com/inward/record.url?scp=85085374785&partnerID=8YFLogxK

U2 - 10.1080/00927872.2020.1764010

DO - 10.1080/00927872.2020.1764010

M3 - Article

AN - SCOPUS:85085374785

SN - 0092-7872

VL - 48

SP - 4457

EP - 4482

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -