000			03169nam a22004095i 4500
003			DE-He213
005			20191013150956.0
007			cr nn 008mamaa
008			100301s2009 gw | s |||| 0|eng d
020	6	4	_a9783642006395 _9978-3-642-00639-5
024	8	7	_a10.1007/978-3-642-00639-5 _2doi
100	8	1	_aRohde, Christian. _eauthor. _9148882
245	9	7	_aCyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication _h[electronic resource] / _cby Christian Rohde.
001			000066143
300	6	4	_bonline resource.
490	8	1	_aLecture Notes in Mathematics, _x0075-8434 ; _v1975
505	8	0	_aAn Introduction to Hodge Structures and Shimura Varieties -- Cyclic Covers of the Projective Line -- Some Preliminaries for Families of Cyclic Covers -- The Galois Group Decomposition of the Hodge Structure -- The Computation of the Hodge Group -- Examples of Families with Dense Sets of Complex Multiplication Fibers -- The Construction of Calabi-Yau Manifolds with Complex Multiplication -- The Degree 3 Case -- Other Examples and Variations -- Examples of Families of 3-manifolds and their Invariants -- Maximal Families of CMCY Type.
520	6	4	_aThe main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.
650	8	0	_aMathematics. _98571
650	8	0	_aGeometry, algebraic. _9148883
650			_aMathematics. _98571
650			_aAlgebraic Geometry. _9148884
710	8	2	_aSpringerLink (Online service) _9148885
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642006388
830	8	0	_aLecture Notes in Mathematics, _x0075-8434 ; _v1975 _9148886
856			_uhttp://dx.doi.org/10.1007/978-3-642-00639-5 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2009.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
516	6	4	_aZDB-2-LNM
999			_c65873 _d65873
942			_c05