000			03641nam a22005655i 4500
001			978-0-8176-4578-6
003			DE-He213
005			20161121231125.0
007			cr nn 008mamaa
008			120414s2007 xxu| s |||| 0|eng d
020			_a9780817645786 _9978-0-8176-4578-6
024	7		_a10.1007/978-0-8176-4578-6 _2doi
050		4	_aQA351
072		7	_aPBKF _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.5 _223
100	1		_aMumford, David. _eauthor.
245	1	0	_aTata Lectures on Theta II _h[electronic resource] / _cby David Mumford.
264		1	_aBoston, MA : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2007.
300			_aXIV, 272 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aAn Elementary Construction of Hyperelliptic Jacobians -- Review of background in algebraic geometry -- Divisors on hyperelliptic curves -- Algebraic construction of the Jacobian of a hyperelliptic curve -- The translation-invariant vector fields -- Neumann’s dynamical system -- Tying together the analytic Jacobian and algebraic Jacobian -- Theta characteristics and the fundamental Vanishing Property -- Frobenius’ theta formula -- Thomae’s formula and moduli of hyperelliptic curves -- Characterization of hyperelliptic period matrices -- The hyperelliptic p-function -- The Korteweg-deVries dynamical system -- Fay’s Trisecant Identity for Jacobian theta functions -- The Prime Form E(x,y). -- Fay’s Trisecant Identity -- Corollaries of the identity -- Applications to solutions of differential equations -- The Generalized Jacobian of a Singular Curve and its Theta Function -- Resolution of algebraic equations by theta constants -- Resolution of algebraic equations by theta constants.
520			_aThe second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.
650		0	_aMathematics.
650		0	_aAlgebraic geometry.
650		0	_aFunctions of complex variables.
650		0	_aPartial differential equations.
650		0	_aSpecial functions.
650		0	_aAlgebraic topology.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aSpecial Functions.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aAlgebraic Topology.
650	2	4	_aPartial Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817645694
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4578-6
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508956 _d508956