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010   $a3-031-25570-4
024 7 $a10.1007/978-3-031-25570-0
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035   $a(DE-He213)978-3-031-25570-0
035   $a(EXLCZ)995580000000524626
100   $a20230315d2023      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAbelian Varieties over the Complex Numbers$b[electronic resource] $eA Graduate Course /$fby Herbert Lange
205   $a1st ed. 2023.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023.
215   $a1 online resource (XII, 384 p. 1 illus.)
225 1 $aGrundlehren Text Editions,$x2627-5260
311   $a3-031-25569-0 
327   $a1. Line Bundles on Complex Tori -- 2 Abelian Varieties -- 3 Moduli Spaces -- 4 Jacobian Varieties -- 5 Main Examples of Abelian Varieties -- 6 The Fourier Transform for Sheaves and Cycles -- 7 Introduction to the Hodge Conjecture for Abelian Varieties.
330   $aThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles. The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier?Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.
410  0$aGrundlehren Text Editions,$x2627-5260
606   $aAlgebraic geometry
606   $aProjective geometry
606   $aFunctions of complex variables
606   $aNumber theory
606   $aAlgebraic Geometry
606   $aProjective Geometry
606   $aFunctions of a Complex Variable
606   $aNumber Theory
606   $aVarietats abelianes$2thub
606   $aNombres complexos$2thub
608   $aLlibres electrònics$2thub
615  0$aAlgebraic geometry.
615  0$aProjective geometry.
615  0$aFunctions of complex variables.
615  0$aNumber theory.
615 14$aAlgebraic Geometry.
615 24$aProjective Geometry.
615 24$aFunctions of a Complex Variable.
615 24$aNumber Theory.
615  7$aVarietats abelianes
615  7$aNombres complexos
676   $a516.35
700   $aLange$b Herbert$4aut$4http://id.loc.gov/vocabulary/relators/aut$059603
906   $aBOOK
912   $a9910682551703321
996   $aAbelian Varieties over the Complex Numbers$93293387
997   $aUNINA