Description
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C -schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C -schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C -schemes with corners'.
About the Author
Kelli Francis-Staite read for her DPhil at the University of Oxford as a Rhodes Scholar. Her thesis developed the theory of C -algebraic geometry with corners. She is currently an Adjunct Senior Lecturer at the University of Adelaide. Dominic Joyce is Professor of Mathematics at Oxford University and a Senior Research Fellow at Lincoln College Oxford. He is the author of 'Compact Manifolds with Special Holonomy' (2000), 'Riemannian Holonomy Groups and Calibrated Geometry' (2007), 'A Theory of Generalized Donaldson-Thomas Invariants' (2012 co-authored with Yinan Song), and 'Algebraic Geometry over C -rings' (2019). Joyce is winner of the LMS Whitehead and Froehlich prizes, an EMS prize, the Adams prize, and he is a Fellow of the Royal Society.
Book Information
ISBN 9781009400169
Author Kelli Francis-Staite
Format Paperback
Page Count 220
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 320g
Dimensions(mm) 229mm * 152mm * 13mm
Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C -schemes with corners'.
About the Author
Kelli Francis-Staite read for her DPhil at the University of Oxford as a Rhodes Scholar. Her thesis developed the theory of C -algebraic geometry with corners. She is currently an Adjunct Senior Lecturer at the University of Adelaide. Dominic Joyce is Professor of Mathematics at Oxford University and a Senior Research Fellow at Lincoln College Oxford. He is the author of 'Compact Manifolds with Special Holonomy' (2000), 'Riemannian Holonomy Groups and Calibrated Geometry' (2007), 'A Theory of Generalized Donaldson-Thomas Invariants' (2012 co-authored with Yinan Song), and 'Algebraic Geometry over C -rings' (2019). Joyce is winner of the LMS Whitehead and Froehlich prizes, an EMS prize, the Adams prize, and he is a Fellow of the Royal Society.
Book Information
ISBN 9781009400169
Author Kelli Francis-Staite
Format Paperback
Page Count 220
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 320g
Dimensions(mm) 229mm * 152mm * 13mm
