Matches in SemOpenAlex for { <https://semopenalex.org/work/W4292174950> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4292174950 abstract "We study the inverse Jacobian problem for the case of Picard curves over $mathbb{C}$. More precisely, we elaborate on an algorithm that, given a small period matrix $Omegain mathbb{C}^{3times 3}$ corresponding to a principally polarized abelian threefold equipped with an automorphism of order $3$, returns a Legendre-Rosenhain equation for a Picard curve with Jacobian isomorphic to the given abelian variety. Our method corrects a formula obtained by Koike-Weng in [Math. Comp., 74(249):499-518, 2005] which is based on a theorem of Siegel. As a result, we apply the algorithm to obtain (numerically) all the isomorphism classes of Picard curves with maximal complex multiplication attached to the sextic CM-fields with class number at most $4$. In particular, we obtain (conjecturally) the complete list of CM Picard curves defined over $mathbb{Q}$. In the appendix, Vincent gives a correction to the generalization of Takase's formula for the inverse Jacobian problem for hyperelliptic curves given in [Balakrishnan-Ionica-Lauter-Vincent, LMS J. Comput. Math., 19(suppl. A):283-300, 2016]." @default.
- W4292174950 created "2022-08-18" @default.
- W4292174950 creator A5014425101 @default.
- W4292174950 creator A5028782012 @default.
- W4292174950 creator A5033391962 @default.
- W4292174950 date "2016-11-08" @default.
- W4292174950 modified "2023-09-24" @default.
- W4292174950 title "An inverse Jacobian algorithm for Picard curves" @default.
- W4292174950 doi "https://doi.org/10.48550/arxiv.1611.02582" @default.
- W4292174950 hasPublicationYear "2016" @default.
- W4292174950 type Work @default.
- W4292174950 citedByCount "0" @default.
- W4292174950 crossrefType "posted-content" @default.
- W4292174950 hasAuthorship W4292174950A5014425101 @default.
- W4292174950 hasAuthorship W4292174950A5028782012 @default.
- W4292174950 hasAuthorship W4292174950A5033391962 @default.
- W4292174950 hasBestOaLocation W42921749501 @default.
- W4292174950 hasConcept C10138342 @default.
- W4292174950 hasConcept C11074058 @default.
- W4292174950 hasConcept C11413529 @default.
- W4292174950 hasConcept C118712358 @default.
- W4292174950 hasConcept C134306372 @default.
- W4292174950 hasConcept C136119220 @default.
- W4292174950 hasConcept C136170076 @default.
- W4292174950 hasConcept C162324750 @default.
- W4292174950 hasConcept C177148314 @default.
- W4292174950 hasConcept C182306322 @default.
- W4292174950 hasConcept C200331156 @default.
- W4292174950 hasConcept C202444582 @default.
- W4292174950 hasConcept C207467116 @default.
- W4292174950 hasConcept C2524010 @default.
- W4292174950 hasConcept C28826006 @default.
- W4292174950 hasConcept C33923547 @default.
- W4292174950 hasConceptScore W4292174950C10138342 @default.
- W4292174950 hasConceptScore W4292174950C11074058 @default.
- W4292174950 hasConceptScore W4292174950C11413529 @default.
- W4292174950 hasConceptScore W4292174950C118712358 @default.
- W4292174950 hasConceptScore W4292174950C134306372 @default.
- W4292174950 hasConceptScore W4292174950C136119220 @default.
- W4292174950 hasConceptScore W4292174950C136170076 @default.
- W4292174950 hasConceptScore W4292174950C162324750 @default.
- W4292174950 hasConceptScore W4292174950C177148314 @default.
- W4292174950 hasConceptScore W4292174950C182306322 @default.
- W4292174950 hasConceptScore W4292174950C200331156 @default.
- W4292174950 hasConceptScore W4292174950C202444582 @default.
- W4292174950 hasConceptScore W4292174950C207467116 @default.
- W4292174950 hasConceptScore W4292174950C2524010 @default.
- W4292174950 hasConceptScore W4292174950C28826006 @default.
- W4292174950 hasConceptScore W4292174950C33923547 @default.
- W4292174950 hasLocation W42921749501 @default.
- W4292174950 hasLocation W42921749502 @default.
- W4292174950 hasLocation W42921749503 @default.
- W4292174950 hasLocation W42921749504 @default.
- W4292174950 hasOpenAccess W4292174950 @default.
- W4292174950 hasPrimaryLocation W42921749501 @default.
- W4292174950 hasRelatedWork W1966681239 @default.
- W4292174950 hasRelatedWork W1970345540 @default.
- W4292174950 hasRelatedWork W2018852123 @default.
- W4292174950 hasRelatedWork W2044058234 @default.
- W4292174950 hasRelatedWork W2070968330 @default.
- W4292174950 hasRelatedWork W2126269293 @default.
- W4292174950 hasRelatedWork W2163750819 @default.
- W4292174950 hasRelatedWork W2625158582 @default.
- W4292174950 hasRelatedWork W3020619612 @default.
- W4292174950 hasRelatedWork W4245905705 @default.
- W4292174950 isParatext "false" @default.
- W4292174950 isRetracted "false" @default.
- W4292174950 workType "article" @default.