000 03324nam a22004455i 4500
001 978-3-642-00639-5
003 DE-He213
005 20190213151745.0
007 cr nn 008mamaa
008 100301s2009 gw | s |||| 0|eng d
020 _a9783642006395
_9978-3-642-00639-5
024 7 _a10.1007/978-3-642-00639-5
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aRohde, Christian.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aCyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
_h[electronic resource] /
_cby Christian Rohde.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aIX, 228 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1975
505 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 _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 0 _aGeometry, algebraic.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642006555
776 0 8 _iPrinted edition:
_z9783642006388
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1975
856 4 0 _uhttps://doi.org/10.1007/978-3-642-00639-5
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11783
_d11783