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## Branes on Poisson Varieties

*Marco Gualtieri*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0018
- Subject:
- Mathematics, Geometry / Topology

This chapter takes a second look at a classical structure in differential and algebraic geometry — that of a holomorphic Poisson structure — which is a complex manifold with a holomorphic Poisson ... More

## Topological Invariants and Differential Geometry

*Paula Tretkoff*

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

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number ... More

## Hodge Representations and Hodge Domains

*Mark Green, Phillip Griffiths, and Matt Kerr*

### in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.003.0005
- Subject:
- Mathematics, Analysis

This chapter deals with Hodge representations and Hodge domains. For general polarized Hodge structures, it considers which semi-simple ℚ-algebraic groups M can be Mumford-Tate groups of polarized ... More

## Introduction to Kähler Manifolds

*Eduardo Cattani and Phillip Griffiths*

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)*

### in Hodge Theory (MN-49)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter provides an introduction to the basic results on the topology of compact Kähler manifolds that underlie and motivate Hodge theory. This chapter consists of five sections which ... More

## Complex manifolds

*Clifford Henry Taubes*

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

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605880.003.0017
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines complex manifolds. It discusses some basics concerning holomorphic functions on ℂn; the definition of a complex manifold; first examples of complex manifolds; the ... More

## The Mumford-Tate Group of a Variation of Hodge Structure

*Mark Green, Phillip Griffiths, and Matt Kerr*

### in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154244
- eISBN:
- 9781400842735
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154244.003.0004
- Subject:
- Mathematics, Analysis

This chapter deals with the Mumford-Tate group of a variation of Hodge structure (VHS). It begins by presenting a definition of VHS, which consists of a connected complex manifold and a locally ... More

## Holomorphic submanifolds, holomorphic sections and curvature

*Clifford Henry Taubes*

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

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605880.003.0018
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

This chapter discusses how complex manifolds and Kähler manifolds can appear as submanifolds in a larger complex or Kähler manifold. It describes holomorphic submanifolds of a complex manifold and ... More

## Introduction

*Araceli Bonifant, Mikhail Lyubich, Scott Sutherland, Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)*

### in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This introductory chapter is an overview into holomorphic dynamics—one of the earliest branches of dynamical systems which is not part of classical mechanics. Holomorphic dynamics studies iterates of ... More

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