MARC Record from marc_columbia

LEADER: 04225cam a2200505Ii 4500
001 15276107
005 20210119105037.0
008 200323s2020 gw a b 001 0 eng d
035 $a(OCoLC)on1145545173
040 $aYDX$beng$erda$cYDX$dOCLCQ$dOCLCF$dFTU$dOCLCO$dKEI$dIPS$dOCL
019 $a1193378950
020 $a3037192089
020 $a9783037192085
024 7 $a10.4171/208$2doi
035 $a(OCoLC)1145545173$z(OCoLC)1193378950
041 1 $aeng$hjpn
050 4 $aQA573$b.K6613 2020
082 04 $a516.3/52$223
084 $a414.73$2njb/10
049 $aZCUA
100 1 $aKondō, Shigeyuki,$d1958-$eauthor.
245 10 $aK3 surfaces /$cShigeyuki Kondō.
264 1 $aBerlin, Germany :$bEuropean Mathematical Society,$c[2020]
264 4 $c©2020
300 $axiii, 236 pages:$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aEMS Tracts in Mathematics ;$v32
500 $a"This book is an extended English version of the author's book "K3 Surfaces" in Japanese, which forms volume 5 of the series 'Suugaku no Kagayaki', published in 2015 by Kyoritsu Shuppan Japan. Chapters 0-10 are an English translation of the above book by the author himself. Chapter 11 and 12 are new and added to the English version by the author." -preface
504 $aIncludes bibliographical references and index.
505 0 $aLattice theory -- Reflection groups and their fundamental domains -- Complex analytic surfaces -- K3 surfaces and examples -- Bounded symmetric domains of type IV and deformations of complexstructures -- The Torelli-type theorem for K3 surfaces -- Surjectivity of the period map of K3 surfaces -- Application of the Torelli-type theorem to automorphisms -- Enriques surfaces -- Application to the moduli space of plane quartic curves -- Finite groups of symplectic automorphisms of K3 surfaces and the Mathieugroup -- Automorphism group of the Kummer surface associated with a curve of genus 2.
520 $aK3 surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 - a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century.K3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods - called the Torelli-type theorem for K3 surfaces - was established around 1970. Since then, several pieces of research on K3 surfaces have been undertaken and more recently K3 surfaces have even become of interest in theoretical physics.The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K3 surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study K3 surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of $K3$ surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice.The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry.
650 0 $aSurfaces, Algebraic.
650 0 $aThreefolds (Algebraic geometry)
650 0 $aGeometry, Algebraic.
650 07 $aAnalytic geometry.$2bicssc
650 7 $aThreefolds (Algebraic geometry)$2fast$0(OCoLC)fst01150346
650 7 $aGeometry, Algebraic.$2fast$0(OCoLC)fst00940902
650 7 $aSurfaces, Algebraic.$2fast$0(OCoLC)fst01139295
650 07 $aAlgebraic geometry.$2msc
650 07 $aSeveral complex variables and analytic spaces.$2msc
830 0 $aEMS tracts in mathematics ;$v32.
880 0 $6765-00$tK3曲面.$d共立出版. 2015.$k数学の輝き ; 5.
852 00 $bmat$hQA573$i.K6613 2020g