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For some reasons, I have to study the Castelnuovo-Mumford regularity.

There are some papers on this regularity, which can be found here : Castelnuovo-Mumford Regularity

My question is: What is the importance of this regularity? What information will we know if we know about the Castelnuovo-Mumford regularity?

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    Well, it helps you prove some things about Hilbert schemes, which seems interesting enough. You might want to look at Mumford's _Curves on an Algebraic Surface_.2012-06-22
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    Have you seen http://mathoverflow.net/questions/80/what-is-interesting-useful-about-castelnuovo-mumford-regularity ?2012-06-22
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    @Quiaochu Yuan : Thanks for pointing it out.2012-06-22

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