Hardcover ISBN:  9783037192085 
Product Code:  EMSTM/32 
List Price:  $88.00 
AMS Member Price:  $70.40 
Hardcover ISBN:  9783037192085 
Product Code:  EMSTM/32 
List Price:  $88.00 
AMS Member Price:  $70.40 

Book DetailsEMS Tracts in MathematicsVolume: 32; 2020; 250 ppMSC: Primary 14; 32
\(K\)3 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. \(K\)3 surfaces can be considered as a 2dimensional analogue of an elliptic curve, and the theory of periods—called the Torellitype theorem for K3 surfaces—was established around 1970. Since then, several pieces of research on \(K\)3 surfaces have been undertaken and more recently \(K\)3 surfaces have even become of interest in theoretical physics.
The main purpose of this book is an introduction to the Torellitype theorem for complex analytic \(K\)3 surfaces and its applications. The theory of lattices and their reflection groups is necessary to study \(K\)3 surfaces, and this book introduces these notions. In addition to lattices and reflection groups, the book contains the classification of complex analytic surfaces, the Torellitype theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of \(K\)3 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 areas 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.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipStudents and researchers interested in algebraic geometry.

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\(K\)3 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. \(K\)3 surfaces can be considered as a 2dimensional analogue of an elliptic curve, and the theory of periods—called the Torellitype theorem for K3 surfaces—was established around 1970. Since then, several pieces of research on \(K\)3 surfaces have been undertaken and more recently \(K\)3 surfaces have even become of interest in theoretical physics.
The main purpose of this book is an introduction to the Torellitype theorem for complex analytic \(K\)3 surfaces and its applications. The theory of lattices and their reflection groups is necessary to study \(K\)3 surfaces, and this book introduces these notions. In addition to lattices and reflection groups, the book contains the classification of complex analytic surfaces, the Torellitype theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of \(K\)3 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 areas 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.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Students and researchers interested in algebraic geometry.