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001451491 019__ $$a1351745263$$a1351746547
001451491 020__ $$a9783031101458$$q(electronic bk.)
001451491 020__ $$a3031101456$$q(electronic bk.)
001451491 020__ $$z9783031101441
001451491 020__ $$z3031101448
001451491 0247_ $$a10.1007/978-3-031-10145-8$$2doi
001451491 035__ $$aSP(OCoLC)1351747467
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001451491 08204 $$a516.3/5$$223/eng/20221208
001451491 1001_ $$aLange, H.$$q(Herbert),$$d1943-$$eauthor.
001451491 24510 $$aDecomposition of Jacobians by Prym varieties /$$cHerbert Lange, Rubí E. Rodríguez.
001451491 264_1 $$aCham :$$bSpringer,$$c[2022]
001451491 264_4 $$c©2022
001451491 300__ $$a1 online resource (xiii, 251 pages) :$$billustrations.
001451491 336__ $$atext$$btxt$$2rdacontent
001451491 337__ $$acomputer$$bc$$2rdamedia
001451491 338__ $$aonline resource$$bcr$$2rdacarrier
001451491 4901_ $$aLecture notes in mathematics ;$$vvolume 2310
001451491 504__ $$aIncludes bibliographical references and index.
001451491 5058_ $$aIntro -- Preface -- Acknowledgements -- Contents -- Notations -- 1 Introduction -- 2 Preliminaries and Basic Results -- 2.1 Line Bundles on Abelian Varieties -- 2.2 Polarized Abelian Varieties -- 2.3 Endomorphisms of Abelian Varieties -- 2.4 The Weil Form on K(L) -- 2.5 Symmetric Idempotents -- 2.6 Abelian Subvarieties of a Polarized Abelian Variety -- 2.6.1 The Principally Polarized Case -- 2.6.2 The Case of an Arbitrary Polarization -- 2.7 Poincaré's Reducibility Theorem -- 2.8 Complex and Rational Representations of Finite Groups -- 2.9 The Isotypical and Group Algebra Decompositions
001451491 5058_ $$a2.9.1 Generalities -- 2.9.2 Induced Action on the Tangent Space -- 2.10 Action of a Hecke Algebra on an Abelian Variety -- 3 Prym Varieties -- 3.1 Finite Covers of Curves -- 3.1.1 Definitions and Elementary Results -- 3.1.2 The Signature of a Galois Cover -- 3.1.3 The Geometric Signature of a Galois Cover -- 3.2 Prym Varieties of Covers of Curves -- 3.2.1 Definition of Prym Varieties -- 3.2.2 Polarizations of Prym Varieties -- 3.2.3 The Degrees of the Decomposition Isogeny -- 3.2.4 Degrees of Isogenies Arising from a Decomposition of f: C""0365C →C
001451491 5058_ $$a3.3 Two-Division Points of Prym Varieties of Double Covers -- 3.4 Prym Varieties of Pairs of Covers -- 3.5 Galois Covers of Curves -- 3.5.1 Jacobians and Pryms of Intermediate Covers -- 3.5.2 Isotypical and Group Algebra Decompositions of Intermediate Covers -- 3.5.3 Decomposition of the Tangent Space of the Prym Variety Associated to a Pair of Subgroups -- 3.5.4 The Dimension of an Isotypical Component -- 4 Covers of Degree 2 and 3 -- 4.1 Covers of Degree 2 -- 4.2 Covers of Degree 3 -- 4.2.1 Cyclic Covers of Degree 3 -- 4.2.2 Non-cyclic Covers of Degree 3: The Galois Closure
001451491 5058_ $$a5.4.1 Definition and First Properties -- 5.4.2 Determination of the Bigonal Construction in the Non-Galois Case -- 5.4.3 The Bigonal Construction over C =P1 -- 5.4.4 Pantazis' Theorem -- 5.5 The Alternating Group of Degree 4 -- 5.5.1 Ramification and Genera -- 5.5.2 Decompositions of J -- 5.5.3 A Generalization of the Trigonal Construction -- 5.6 The Trigonal Construction for Covers with Group A4 -- 5.7 The Symmetric Group S4 -- 5.7.1 Ramification and Genera -- 5.7.2 Decomposition of J""0365J -- 5.7.3 Isogenies Arising from Actions of Subgroups of S4 -- 5.7.4 An Isogeny Arising from the Action of a Quotient of S4.
001451491 506__ $$aAccess limited to authorized users.
001451491 520__ $$aThis monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.
001451491 588__ $$aDescription based upon print version of record.
001451491 650_0 $$aJacobians.
001451491 650_0 $$aGeometry, Algebraic.
001451491 650_0 $$aCurves, Algebraic.
001451491 655_0 $$aElectronic books.
001451491 7001_ $$aRodríguez, Rubí E.,$$d1953-$$eauthor.
001451491 77608 $$iPrint version:$$aLange, Herbert$$tDecomposition of Jacobians by Prym Varieties$$dCham : Springer International Publishing AG,c2022$$z9783031101441
001451491 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2310.
001451491 852__ $$bebk
001451491 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-10145-8$$zOnline Access$$91397441.1
001451491 909CO $$ooai:library.usi.edu:1451491$$pGLOBAL_SET
001451491 980__ $$aBIB
001451491 980__ $$aEBOOK
001451491 982__ $$aEbook
001451491 983__ $$aOnline
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