Complex Ball Quotients and Line Arrangements in the Projective Plane (eBook)

Paula Tretkoff (Autor)

eBook Download: EPUB

2016
232 Seiten
Princeton University Press (Verlag)
978-1-4008-8125-3 (ISBN)

Infos

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function.The material in this book began as a set of lecture notes, taken by Tretkoff, of a course given by Friedrich Hirzebruch at ETH Zurich in 1996. The lecture notes were then considerably expanded by Hirzebruch and Tretkoff over a number of years. In this book, Tretkoff has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers.Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.

Autor

Paula Tretkoff is professor of mathematics at Texas A&M University and director of research in the National Center for Scientific Research (CNRS) at the Université de Lille 1, France.

Produkt-Details

• Erscheint lt. Verlag: 16.2.2016
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Mitarbeit: Anhang von: Hans-Christoph Im Hof
• Zusatzinfo: 2 line illus. 18 tables.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Adjunction formula • Algebraic Geometry • algebraic group • algebraic surface • algebraic variety • Appell hypergeometric function • arithmetic monodromy group • automorphism • ball quotient • Betti number • b-space • Canonical bundle • canonical divisor class • Cardinality • Chern numbers • Codimension • coefficient • cohomology • Compactification (mathematics) • Compact Riemann surface • complete quadrilateral • complex 2-ball • Complex Analysis • Complex dimension • complex manifold • complex number • complex plane • Complex projective plane • Complex Surface • conjecture • conjugacy class • Connected space • covering group • Covering space • Curvature • de Rham cohomology • differential equation • differential form • Differential Geometry • differential geometry of surfaces • Dimension • Division by zero • Divisor • Divisor (algebraic geometry) • divisor class group • Elliptic Curve • Elliptic Surface • Embedding • equivalence class • equivalence relation • Euler number • finite covering • finite group • Finite set • first Chern class • fractional linear transformation • free 2-ball quotient • Friedrich Hirzebruch • Fuchsian group • Fundamental domain • fundamental group • Gauss hypergeometric function • Gaussian curvature • Geometry • Hermitian matrix • Hermitian metric • holomorphic function • Homogeneous Coordinates • Homology (mathematics) • Homomorphism • Homotopy • hypergeometric function • icosahedron • Inner automorphism • intersection point • Intersection (set theory) • Intersection theory • Kodaira Dimension • Lie group • Linear algebraic group • linear arrangement • line arrangement • line bundle • log-canonical divisor • manifold • Mbius transformation • Meromorphic Function • minimal surface • Miyaoka-Yau inequality • Monodromy • Monodromy group • Natural number • Non-Euclidean geometry • normal subgroup • Open set • orbifold • orbifold structure • partial differential equation • Permutation • plurigenus • polynomial • Princeton University • Projective line • projective plane • projective space • projective variety • proportionality deviation • quadratic form • Quotient space (topology) • ramification indices • rational curve • regular point • Ricci curvature • Riemannian metric • Riemann sphere • Riemann surface • sectional curvature • signature • Smoothness • Solution Space • Special case • SUBGROUP • submanifold • Summation • Surface of general type • Surjective function • Tangent Space • Theorem • topological invariant • Topological space • transversely intersecting divisor • Triangle group • Triangle groups • Triple Point • two-dimensional space • uniformization theorem • Unit disk • Vector Space • Volume form • weight
• ISBN-10: 1-4008-8125-0 / 1400881250
• ISBN-13: 978-1-4008-8125-3 / 9781400881253