Home
Hostname: page-component-6c8bd87754-ncgjf Total loading time: 0.262 Render date: 2022-01-16T20:14:00.214Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

# 15 - Some algebraic geometry

Published online by Cambridge University Press:  05 September 2012

## Summary

In chapters 12 and 14 we developed some simple tools in differential geometry and used them to gain some insight concerning the compactification of hidden dimensions as well as some insight concerning phenomena on the string world sheet. We now turn our attention to some more specialized mathematical tools involving complex manifolds and algebraic geometry. Again, the motivation is twofold. The world sheet of a string is a complex manifold – a Riemann surface, in fact – and as string theory develops, the deeper study of world-sheet phenomena is likely to involve deeper aspects of algebraic geometry, which have already begun to enter in recent works on multiloop diagrams. Also, algebraic geometry has been a tool in recent attempts to formulate more realistic models of string compactification.

In this chapter, we develop some of the basic concepts of complex geometry, with examples selected for their role both in world-sheet phenomena and in the study of compactification. We will unfortunately not be able to describe in this book recent work on the application of algebraic geometry to multi-loop diagrams. This subject is probably not yet ripe for synthesis; and the requisite mathematical machinery is more extensive than we will be able to present even in this moderately lengthy chapter. By laying at least some of the elementary foundations we hope to facilitate the task of the reader who wishes to delve further elsewhere.

Type
Chapter
Information
Superstring Theory
25th Anniversary Edition
, pp. 413 - 474
Publisher: Cambridge University Press
Print publication year: 2012

## Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

### Purchase

Buy print or eBook[Opens in a new window]

# Send book to Kindle

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

# Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

# Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×