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In mathematics, a '''quintic threefold''' is a degree 5 dimension 3 hypersurface in 4-dimensional projective space. Non-singular quintic threefolds are [[Calabi–Yau manifold]]s.


The [[Hodge diamond]] of a non-singular quintic 3-fold is
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==Rational curves==
If you are looking for a specific plugin, then you can just search for the name of the plugin. Affilo - Theme is the guaranteed mixing of wordpress theme that Mark Ling use for his internet marketing career. PSD files are incompatible to browsers and are suppose to be converted into wordpress compatible files so that it opens up in browser. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. In the most current edition you can customize your retailer layout and display hues and fonts similar to your site or blog. <br><br>These websites can be easily customized and can appear in the top rankings of the major search engines. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Which is perfect for building a mobile site for business use. They provide many such popular products which you can buy for your baby. For a Wordpress website, you don't need a powerful web hosting account to host your site. <br><br>Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. But if you are not willing to choose cost to the detriment of quality, originality and higher returns, then go for a self-hosted wordpress blog and increase the presence of your business in this new digital age. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. Enough automated blog posts plus a system keeps you and your clients happy. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>You can add keywords but it is best to leave this alone. High Quality Services: These companies help you in creating high quality Word - Press websites. Some examples of its additional features include; code inserter (for use with adding Google Analytics, Adsense section targeting etc) Webmaster verification assistant, Link Mask Generator, Robots. If you loved this write-up and you would such as to get additional facts concerning [http://s.do-dance.com/wordpressbackup353895 backup plugin] kindly browse through the web site. It supports backup scheduling and allows you to either download the backup file or email it to you. The Pakistani culture is in demand of a main surgical treatment. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. An ease of use which pertains to both internet site back-end and front-end users alike. However, you must also manually approve or reject comments so that your website does not promote parasitic behavior. If this is not possible you still have the choice of the default theme that is Word - Press 3. For your information, it is an open source web content management system.
{{harvtxt|Clemens|1984}} conjectured that the number of rational curves of a given degree on a generic quintic threefold is finite. (Some smooth but non-generic quintic threefolds have infinite families of lines on them.) This was verified for degrees up to 7 by {{harvtxt|Katz|1986}} who also calculated the number 609250 of degree 2 rational curves.  
{{harvs||txt| last1=Candelas | first1=Philip | last2=de la Ossa | first2=Xenia C. | last3=Green | first3=Paul S. | last4=Parkes | first4=Linda | title=A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory | doi=10.1016/0550-3213(91)90292-6  | id={{MathSciNet | id = 1115626}} | year=1991 | journal=Nuclear Physics. B | issn=0550-3213 | volume=359 | issue=1 | pages=21–74}}
conjectured a general formula for the number of rational curves of any degree, which was proved by {{harvtxt|Givental|1996}}
The number of rational curves of various degrees on a generic quintic threefold is given by  
:5, 2875, 609250, 317206375, 242467530000, ...{{OEIS|A076912}}.
Since the generic quintic threefold is a Calabi–Yau threefold and the moduli space of rational curves of a given degree is a discrete, finite set (hence compact), these have well-defined [[Donaldson–Thomas invariant]]s (the "virtual number of points"); at least for degree 1 and 2, these agree with the actual number of points.
 
==Examples==
*The [[Fermat quintic threefold]] is given by <math>V^5+W^5+X^5+Y^5+Z^5=0</math>.
*[[Barth–Nieto quintic]]
 
==References==
*{{Citation | last1=Candelas | first1=Philip | last2=de la Ossa | first2=Xenia C. | last3=Green | first3=Paul S. | last4=Parkes | first4=Linda | title=A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory | doi=10.1016/0550-3213(91)90292-6  | id={{MathSciNet | id = 1115626}} | year=1991 | journal=Nuclear Physics. B | issn=0550-3213 | volume=359 | issue=1 | pages=21–74}}
*{{Citation | last1=Clemens | first1=Herbert | title=Topics in transcendental algebraic geometry (Princeton, N.J., 1981/1982) | publisher=[[Princeton University Press]] | series=Ann. of Math. Stud. | id={{MathSciNet | id = 756858}} | year=1984 | volume=106 | chapter=Some results about Abel-Jacobi mappings | pages=289–304}}
*{{Citation | last1=Cox | first1=David A. | last2=Katz | first2=Sheldon | title=Mirror symmetry and algebraic geometry | url=http://www.ams.org/bookstore-getitem/item=surv-68.s | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=Mathematical Surveys and Monographs | isbn=978-0-8218-1059-0 | id={{MathSciNet | id = 1677117}} | year=1999 | volume=68}}
*{{Citation | last1=Givental | first1=Alexander B. | title=Equivariant Gromov-Witten invariants | doi=10.1155/S1073792896000414 | id={{MathSciNet | id = 1408320}} | year=1996 | journal=International Mathematics Research Notices | issn=1073-7928 | issue=13 | pages=613–663 | volume=1996}}
*{{Citation | last1=Katz | first1=Sheldon | title=On the finiteness of rational curves on quintic threefolds | url=http://www.numdam.org/item?id=CM_1986__60_2_151_0 | id={{MathSciNet | id = 868135}} | year=1986 | journal=Compositio Mathematica | issn=0010-437X | volume=60 | issue=2 | pages=151–162}}
*{{Citation | last1=Pandharipande | first1=Rahul | title=Rational curves on hypersurfaces (after A. Givental) | url=http://www.numdam.org/item?id=SB_1997-1998__40__307_0 | id={{MathSciNet | id = 1685628}} | year=1998 | journal=Astérisque | issn=0303-1179 | issue=252 | pages=307–340}}
 
[[Category:Algebraic varieties]]
[[Category:Threefolds]]
[[Category:Complex manifolds]]

Latest revision as of 16:24, 28 October 2014


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