Versor (physics): Difference between revisions

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{{DISPLAYTITLE:&lambda;<sub>''g''</sub> conjecture}}
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In algebraic geometry, the '''<math>\lambda_g</math>-conjecture''' gives a particularly simple formula for certain integrals on the Deligne–Mumford compactification <math>\overline{\mathcal M}_{g, n}</math> of the [[moduli space of curves]] with marked points. It was first found as a consequence of the [[Virasoro conjecture]] by {{harvs|txt|first=E. |last=Getzler |first2=R. |last2=Pandharipande |id={{ArXiv|math.AG|9805114}} |title=Virasoro constraints and the Chern classes of the Hodge bundle|journal=Nuclear Phys. |volume=B530 |issue=3|pages=701–714 |year=1998 }}. Later, it was proven by {{harvs|txt | first=C. |last=Faber |first2=R. |last2=Pandharipande |id={{ArXiv|math.AG|9805114}} |title=Hodge integrals, partition matrices, and the <math>\lambda_g</math> conjecture|journal=Ann. of Math. (2)|volume=157 |issue=1|pages=97–124 |year=2003 }} using virtual localization in [[Gromov–Witten theory]]. It is named after the factor of <math>\lambda_g</math>, the ''g''th [[Chern class]] of the [[Hodge bundle]], appearing in its integrand. The other factor is a monomial in the <math>\psi_i</math>, the first Chern classes of the ''n'' cotangent line bundles, as in [[Witten's conjecture]].
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Let ''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub> be positive integers whose sum is 2''g''&nbsp;&minus;&nbsp;3&nbsp;+&nbsp;''n''. Then the <math>\lambda_g</math>-formula says that
 
: <math>\int\limits_{\overline{\mathcal M}_{g, n}} \psi_1^{a_i} \cdot \dots \cdot \psi_n^{a_n}\lambda_g = \binom{2g + n - 3}{a_1, \dots, a_n} \int\limits_{\overline{\mathcal M}_{g, 1}} \psi_1^{2g - 2}\lambda_g.</math>
 
Together with the formula
 
:<math>\int\limits_{\overline{\mathcal M}_{g, 1}} \psi_1^{2g - 2}\lambda_g = \frac{2^{2g - 1} - 1}{2^{2g - 1}} \frac{|B_{2g}|}{(2g)!},</math>
 
where the ''B''<sub>2''g''</sub> are [[Bernoulli number]]s, therefore the <math>\lambda_g</math>-formula gives a way to calculate all integrals on <math>\overline{\mathcal M}_{g, n}</math> involving products in <math>\psi</math>-classes and a factor of <math>\lambda_g</math>.
 
== References ==
 
{{reflist}}
 
*{{Citation | first=E. |last=Pandharipande |first2=R. |last2=Pandharipande |title=Virasoro constraints and the Chern classes of the Hodge bundle|journal=Nuclear Phys. |volume=B530 |issue=3|pages=701–714 |year=1998 | arxiv=math.AG/9805114 | bibcode=1998NuPhB.530..701G | doi=10.1016/S0550-3213(98)00517-3 }}
*{{Citation | first=C. |last=Faber |first2=R. |last2=Pandharipande |title=Hodge integrals, partition matrices, and the <math>\lambda_g</math> conjecture|journal=Ann. Of Math. (2)|volume=157 |issue=1|pages=97–124 |year=2003 | arxiv=math.AG/9805114 | doi=10.4007/annals.2003.157.97 }}
 
[[Category:Algebraic curves]]
[[Category:Moduli theory]]

Latest revision as of 17:45, 6 January 2015

After this Hindi Samachar become widely popular amongst Indians. One great site that is directed at wedding industry professionals is a site called gettingmarriednews. Due to layoffs and cutbacks from full-time employment many people, including myself, are juggling multiple jobs as well as new business ventures and creative projects. With the Hindi newspapers you will be able to remain in touch with all the happenings in the world around. And this is at the same time that concerns are being expressed about the ethical vacuum that the great leader left in his wake. You are allowed to post comments, views and watch videos of world breaking news through these online news channels.

These channels telecast programs in local language for example the people from Jammu Kashmir could get the Jammu Kashmir news in Hindi and it could even reach the rural areas. We give you the advance knowledge of the SEC procedures undertaken by the company so that you can take the advantage in buying and selling of the stock. Indeed Hindi is the mother language of the Indian people. This mechanism replaces the narrow filter of the local newspaper editor and spreads this responsibility among the masses. In the day to day interactions with people, telecom plays a substantial role. Article Source: your FREE Instant Access to 2 of my Instant Article Creation Templates when you visit You'll get get two "plug-n-play" article templates - just plug in your info.

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