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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_97833197_v_n_p51_Bohm |
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todo:paper_97833197_v_n_p51_Bohm2023-10-03T16:45:04Z Local to global algorithms for the gorenstein adjoint ideal of a curve Böhm, J. Decker, W. Laplagne, S. Pfister, G. 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. CHAP info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Böhm, J. Decker, W. Laplagne, S. Pfister, G. 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. |
| format |
CHAP |
| author |
Böhm, J. Decker, W. Laplagne, S. Pfister, G. |
| author_facet |
Böhm, J. Decker, W. Laplagne, S. Pfister, G. |
| author_sort |
Böhm, J. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_97833197_v_n_p51_Bohm |
| work_keys_str_mv |
AT bohmj localtoglobalalgorithmsforthegorensteinadjointidealofacurve AT deckerw localtoglobalalgorithmsforthegorensteinadjointidealofacurve AT laplagnes localtoglobalalgorithmsforthegorensteinadjointidealofacurve AT pfisterg localtoglobalalgorithmsforthegorensteinadjointidealofacurve |
| _version_ |
1807316443601043456 |