LEADER 05696nam 22007455 450 001 9910144598403321 005 20250724090653.0 010 $a3-540-44576-5 024 7 $a10.1007/3-540-44576-5 035 $a(CKB)1000000000233209 035 $a(SSID)ssj0000324045 035 $a(PQKBManifestationID)12133614 035 $a(PQKBTitleCode)TC0000324045 035 $a(PQKBWorkID)10305168 035 $a(PQKB)10126227 035 $a(DE-He213)978-3-540-44576-0 035 $a(MiAaPQ)EBC3071851 035 $a(PPN)155223097 035 $a(BIP)7312785 035 $a(EXLCZ)991000000000233209 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntegrable Systems in the Realm of Algebraic Geometry /$fby Pol Vanhaecke 205 $a2nd ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XII, 264 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1638 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-42337-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Integrable Hamiltonian systems on affine Poisson varietie: Affine Poisson varieties and their morphisms; Integrable Hamiltonian systems and their morphisms; Integrable Hamiltonian systems on other spaces -- Integrable Hamiltonian systems and symmetric products of curves: The systems and their integrability; The geometry of the level manifolds -- Interludium: the geometry of Abelian varieties: Divisors and line bundles; Abelian varieties; Jacobi varieties; Abelian surfaces of type (1,4) -- Algebraic completely integrable Hamiltonian systems: A.c.i. systems; Painlev analysis for a.c.i. systems; The linearization of two-dimensional a.c.i. systems; Lax equations -- The Mumford systems: Genesis; Multi-Hamiltonian structure and symmetries; The odd and the even Mumford systems; The general case -- Two-dimensional a.c.i. systems and applications: The genus two Mumford systems; Application: generalized Kummersurfaces; The Garnier potential; An integrable geodesic flow on SO(4);... 330 $a2. Divisors and line bundles ........................ 99. 2.1. Divisors .............................. 99. 2.2. Line bundles ............................ 100. 2.3. Sections of line bundles ....................... 101. 2.4. The Riemann-Roch Theorem ..................... 103. 2.5. Line bundles and embeddings in projective space ............ 105. 2.6. Hyperelliptic curves ......................... 106. 3. Abelian varieties ............................ 108. 3.1. Complex tori and Abelian varieties .................. 108. 3.2. Line bundles on Abelian varieties ................... 109. 3.3. Abelian surfaces .......................... 111. 4. Jacobi varieties ............................. 114. 4.1. The algebraic Jacobian ....................... 114. 4.2. The analytic/transcendental Jacobian ................. 114. 4.3. Abel's Theorem and Jacobi inversion ................. 119. 4.4. Jacobi and Kummer surfaces ..................... 121. 5. Abelian surfaces of type (1,4) ....................... 123. 5.1. The generic case .......................... 123. 5.2. The non-generic case ........................ 124. V. Algebraic completely integrable Hamiltonian systems ........ 127. 1. Introduction .............................. 127. 2. A.c.i. systems ............................. 129. 3. Painlev~ analysis for a.c.i, systems .................... 135. 4. The linearization of two-dkmensional a.e.i, systems ............. 138. 5. Lax equations ............................. 140. VI. The Mumford systems ..................... 143. 1. Introduction .............................. 143. 2. Genesis ................................ 145. 2.1. The algebra of pseudo-differential operators .............. 145. 2.2. The matrix associated to two commuting operators ........... 146. 2.3. The inverse construction ....................... 150. 2.4. The KP vector fields ........................ 152. ix 3. Multi-Hamiltonian structure and symmetries ................ 155. 3.1. The loop algebra 9(q ........................ 155. 3.2. Reducing the R-brackets and the vector field ~ ............. 157. 4. The odd and the even Mumford systems .................. 161. 4.1. The (odd) Mumford system ..................... 161. 4.2. The even Mumford system ...................... 163. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1638 606 $aDynamics 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aGeometry, Algebraic 606 $aMathematical physics 606 $aDynamical Systems 606 $aGlobal Analysis and Analysis on Manifolds 606 $aAlgebraic Geometry 606 $aTheoretical, Mathematical and Computational Physics 615 0$aDynamics. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aGeometry, Algebraic. 615 0$aMathematical physics. 615 14$aDynamical Systems. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aAlgebraic Geometry. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a516.353 686 $a14K20$2msc 700 $aVanhaecke$b Pol$4aut$4http://id.loc.gov/vocabulary/relators/aut$061070 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144598403321 996 $aIntegrable systems in the realm of algebraic geometry$9258921 997 $aUNINA