Matches in SemOpenAlex for { <https://semopenalex.org/work/W2506185004> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W2506185004 endingPage "219" @default.
- W2506185004 startingPage "209" @default.
- W2506185004 abstract "Let C be a smooth projective (irreducible) curve of genus g over an algebraically closed field k. By Pic(C) (resp. Picd (C)) we denote the Picard group of C (resp. the degree d subset in it). In this chapter we introduce the structure of abelian variety on Pic0(C). More precisely, we construct an abelian variety J = J (C) called the Jacobian of C, such that the group of k-points of J is isomorphic to Pic0(C). The idea is to use the fact that every line bundle of degree g on C has a nonzero global section and that for generic line bundle L of degree g this section is unique (up to rescaling). Therefore, a big subset in Picg(C) can be described in terms of effective divisors on C. The set of effective divisors of degree d on C can be identified with the set of k-points of the symmetric power SymdC (the definition and the main properties of the varieties SymdC are given in Section 16.1). The subset in Picg(C) consisting of line bundles L with h0(L) = 1 corresponds to the set of k-points of an open subset in SymgC. Translating this subset by various line bundles of degree –g we obtain algebraic charts for Pic0(C). We define the Jacobian variety J by gluing these open charts." @default.
- W2506185004 created "2016-08-23" @default.
- W2506185004 creator A5072175999 @default.
- W2506185004 date "2003-04-21" @default.
- W2506185004 modified "2023-09-26" @default.
- W2506185004 title "Construction of the Jacobian" @default.
- W2506185004 doi "https://doi.org/10.1017/cbo9780511546532.017" @default.
- W2506185004 hasPublicationYear "2003" @default.
- W2506185004 type Work @default.
- W2506185004 sameAs 2506185004 @default.
- W2506185004 citedByCount "0" @default.
- W2506185004 crossrefType "book-chapter" @default.
- W2506185004 hasAuthorship W2506185004A5072175999 @default.
- W2506185004 hasConcept C105795698 @default.
- W2506185004 hasConcept C111919701 @default.
- W2506185004 hasConcept C114614502 @default.
- W2506185004 hasConcept C118615104 @default.
- W2506185004 hasConcept C121332964 @default.
- W2506185004 hasConcept C134306372 @default.
- W2506185004 hasConcept C136170076 @default.
- W2506185004 hasConcept C136197465 @default.
- W2506185004 hasConcept C137134375 @default.
- W2506185004 hasConcept C182327082 @default.
- W2506185004 hasConcept C186219872 @default.
- W2506185004 hasConcept C200331156 @default.
- W2506185004 hasConcept C202444582 @default.
- W2506185004 hasConcept C203701370 @default.
- W2506185004 hasConcept C24890656 @default.
- W2506185004 hasConcept C2775997480 @default.
- W2506185004 hasConcept C2780129039 @default.
- W2506185004 hasConcept C28826006 @default.
- W2506185004 hasConcept C33923547 @default.
- W2506185004 hasConcept C41008148 @default.
- W2506185004 hasConcept C46709022 @default.
- W2506185004 hasConcept C51544822 @default.
- W2506185004 hasConcept C62139920 @default.
- W2506185004 hasConcept C78045399 @default.
- W2506185004 hasConcept C95857938 @default.
- W2506185004 hasConceptScore W2506185004C105795698 @default.
- W2506185004 hasConceptScore W2506185004C111919701 @default.
- W2506185004 hasConceptScore W2506185004C114614502 @default.
- W2506185004 hasConceptScore W2506185004C118615104 @default.
- W2506185004 hasConceptScore W2506185004C121332964 @default.
- W2506185004 hasConceptScore W2506185004C134306372 @default.
- W2506185004 hasConceptScore W2506185004C136170076 @default.
- W2506185004 hasConceptScore W2506185004C136197465 @default.
- W2506185004 hasConceptScore W2506185004C137134375 @default.
- W2506185004 hasConceptScore W2506185004C182327082 @default.
- W2506185004 hasConceptScore W2506185004C186219872 @default.
- W2506185004 hasConceptScore W2506185004C200331156 @default.
- W2506185004 hasConceptScore W2506185004C202444582 @default.
- W2506185004 hasConceptScore W2506185004C203701370 @default.
- W2506185004 hasConceptScore W2506185004C24890656 @default.
- W2506185004 hasConceptScore W2506185004C2775997480 @default.
- W2506185004 hasConceptScore W2506185004C2780129039 @default.
- W2506185004 hasConceptScore W2506185004C28826006 @default.
- W2506185004 hasConceptScore W2506185004C33923547 @default.
- W2506185004 hasConceptScore W2506185004C41008148 @default.
- W2506185004 hasConceptScore W2506185004C46709022 @default.
- W2506185004 hasConceptScore W2506185004C51544822 @default.
- W2506185004 hasConceptScore W2506185004C62139920 @default.
- W2506185004 hasConceptScore W2506185004C78045399 @default.
- W2506185004 hasConceptScore W2506185004C95857938 @default.
- W2506185004 hasLocation W25061850041 @default.
- W2506185004 hasOpenAccess W2506185004 @default.
- W2506185004 hasPrimaryLocation W25061850041 @default.
- W2506185004 hasRelatedWork W2182977814 @default.
- W2506185004 hasRelatedWork W2192119462 @default.
- W2506185004 hasRelatedWork W2937460226 @default.
- W2506185004 hasRelatedWork W2952236804 @default.
- W2506185004 hasRelatedWork W2952845791 @default.
- W2506185004 hasRelatedWork W3098664699 @default.
- W2506185004 hasRelatedWork W3126773016 @default.
- W2506185004 hasRelatedWork W4302966916 @default.
- W2506185004 hasRelatedWork W76526463 @default.
- W2506185004 hasRelatedWork W776536739 @default.
- W2506185004 isParatext "false" @default.
- W2506185004 isRetracted "false" @default.
- W2506185004 magId "2506185004" @default.
- W2506185004 workType "book-chapter" @default.