Local to global algorithms for the gorenstein adjoint ideal of a curve

We present new algorithms for computing adjoint ideals of curves and thus, in the planar case, adjoint curves. With regard to terminology, we follow Gorenstein who states the adjoint condition in terms of conductors. Our main algorithmyields the Gorenstein adjoint ideal ℘ of a given curve as the int...

Descripción completa

Guardado en:
Detalles Bibliográficos
Publicado: 2018
Materias:
Adjoint ideals
Algebraic curves
Singularities
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97833197_v_n_p51_Bohm
http://hdl.handle.net/20.500.12110/paper_97833197_v_n_p51_Bohm
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_97833197_v_n_p51_Bohm
record_format dspace
spelling paper:paper_97833197_v_n_p51_Bohm2023-06-08T16:38:54Z Local to global algorithms for the gorenstein adjoint ideal of a curve Adjoint ideals Algebraic curves Singularities We present new algorithms for computing adjoint ideals of curves and thus, in the planar case, adjoint curves. With regard to terminology, we follow Gorenstein who states the adjoint condition in terms of conductors. Our main algorithmyields the Gorenstein adjoint ideal ℘ of a given curve as the intersection of what we call local Gorenstein adjoint ideals. Since the respective local computations do not depend on each other, our approach is inherently parallel. Over the rationals, further parallelization is achieved by a modular version of the algorithm which first computes a number of the characteristic p counterparts of ℘ and then lifts these to characteristic zero. As a key ingredient, we establish an efficient criterion to verify the correctness of the lift.Well-known applications are the computation of Riemann- Roch spaces, the construction of points in moduli spaces, and the parametrization of rational curves. We have implemented different variants of our algorithms together with Mnuk’s approach in the computer algebra system SINGULAR and give timings to compare the performance. © Springer International Publishing AG, part of Springer Nature 2017. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97833197_v_n_p51_Bohm http://hdl.handle.net/20.500.12110/paper_97833197_v_n_p51_Bohm
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Adjoint ideals
Algebraic curves
Singularities
spellingShingle Adjoint ideals
Algebraic curves
Singularities
Local to global algorithms for the gorenstein adjoint ideal of a curve
topic_facet Adjoint ideals
Algebraic curves
Singularities
description We present new algorithms for computing adjoint ideals of curves and thus, in the planar case, adjoint curves. With regard to terminology, we follow Gorenstein who states the adjoint condition in terms of conductors. Our main algorithmyields the Gorenstein adjoint ideal ℘ of a given curve as the intersection of what we call local Gorenstein adjoint ideals. Since the respective local computations do not depend on each other, our approach is inherently parallel. Over the rationals, further parallelization is achieved by a modular version of the algorithm which first computes a number of the characteristic p counterparts of ℘ and then lifts these to characteristic zero. As a key ingredient, we establish an efficient criterion to verify the correctness of the lift.Well-known applications are the computation of Riemann- Roch spaces, the construction of points in moduli spaces, and the parametrization of rational curves. We have implemented different variants of our algorithms together with Mnuk’s approach in the computer algebra system SINGULAR and give timings to compare the performance. © Springer International Publishing AG, part of Springer Nature 2017.
title Local to global algorithms for the gorenstein adjoint ideal of a curve
title_short Local to global algorithms for the gorenstein adjoint ideal of a curve
title_full Local to global algorithms for the gorenstein adjoint ideal of a curve
title_fullStr Local to global algorithms for the gorenstein adjoint ideal of a curve
title_full_unstemmed Local to global algorithms for the gorenstein adjoint ideal of a curve
title_sort local to global algorithms for the gorenstein adjoint ideal of a curve
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97833197_v_n_p51_Bohm
http://hdl.handle.net/20.500.12110/paper_97833197_v_n_p51_Bohm
_version_ 1769175803031977984

Ejemplares similares