LEADER 03585nam 2200589Ia 450 001 9910484386803321 005 20200520144314.0 010 $a1-280-38430-1 010 $a9786613562227 010 $a3-642-00639-6 024 7 $a10.1007/978-3-642-00639-5 035 $a(CKB)1000000000753944 035 $a(SSID)ssj0000317089 035 $a(PQKBManifestationID)11292334 035 $a(PQKBTitleCode)TC0000317089 035 $a(PQKBWorkID)10287273 035 $a(PQKB)10063133 035 $a(DE-He213)978-3-642-00639-5 035 $a(MiAaPQ)EBC3064270 035 $a(PPN)136306144 035 $a(EXLCZ)991000000000753944 100 $a20090518d2009 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aCyclic coverings, Calabi-Yau manifolds and complex multiplication /$fJan Christian Rohde 205 $a1st ed. 2009. 210 $aBerlin $cSpringer$dc2009 215 $a1 online resource (IX, 228 p.) 225 0 $aLecture notes in mathematics,$x0075-8434 ;$v1975 300 $aRevision of work originally presented as the author's thesis (doctoral)--University of Duisburg-Essen, 2007. 311 $a3-642-00638-8 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1975 606 $aCalabi-Yau manifolds 606 $aMultiplication, Complex 615 0$aCalabi-Yau manifolds. 615 0$aMultiplication, Complex. 676 $a516.35 700 $aRohde$b Jan Christian$0319937 712 02$aUniversitat Duisburg-Essen. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484386803321 996 $aCyclic coverings, Calabi-Yau manifolds and complex multiplication$9784542 997 $aUNINA