## Algebraic and Geometric Surgery

*Andrew Ranicki*

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198509240
- eISBN:
- 9780191708725
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509240.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book is an introduction to surgery theory, the standard algebraic topology classification method for manifolds of dimension greater than 4. It is aimed at those who have already been on a basic ... More

## The Ambient Metric (AM-178)

*Charles Fefferman and C. Robin Graham*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153131
- eISBN:
- 9781400840588
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153131.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ... More

## Arithmetic Compactifications of PEL-Type Shimura Varieties

*Kai-Wen Lan*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691156545
- eISBN:
- 9781400846016
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691156545.001.0001
- Subject:
- Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More

## Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

*Claire Voisin*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160504
- eISBN:
- 9781400850532
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160504.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. ... More

## Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

*Paula Tretkoff*

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More

## The Decomposition of Global Conformal Invariants (AM-182)

*Spyros Alexakis*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153476
- eISBN:
- 9781400842728
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153476.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More

## Differential Geometry: Bundles, Connections, Metrics and Curvature

*Clifford Henry Taubes*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199605880
- eISBN:
- 9780191774911
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605880.001.0001
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the ... More

## Flips for 3-folds and 4-folds

*Alessio Corti (ed.)*

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198570615
- eISBN:
- 9780191717703
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570615.001.0001
- Subject:
- Mathematics, Geometry / Topology

The minimal model program in algebraic geometry is a conjectural sequence of algebraic surgery operations that simplifies any algebraic variety to a point where it can be decomposed into pieces with ... More

## Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

*Isroil A. Ikromov and Detlef Müller*

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.001.0001
- Subject:
- Mathematics, Geometry / Topology

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all ... More

## Fourier-Mukai Transforms in Algebraic Geometry

*D. Huybrechts*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this ... More