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Title	O_X regularity bound for smooth varieties with classification of extremal and next to extremal examples
Creator	Kwak, Sijong
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-06-29T09:01
Description	For a smooth variety $X$ and a very ample line bundle $\mathcal L$, $\mathcal O_X$ is $m$-regular with respect to $\mathcal L$ if $H^i(X, \mathcal L^{m-i})=0$ for all $i\ge 1$ and $reg_{\mathcal L}(\mathcal O_X):=\{m \mid \mathcal O_X \text{is $m$-regular}\}.$ For an embedded $n$-dimensional smooth variety $X$ in $\Bbb P^{n+e}$, Eisenbud-Goto conjecture tells us that $reg_{\mathcal L}(\mathcal O_X)\le deg(X)-codim(X)$. We will show that this conjecture is true for smooth varieties and classify boundary cases. On the other hand, there are many counterexamples for singular varieties due to McCullough and Peeva so that it would be desirable to understand the dichotomy between singular cases and smooth cases and how hard to show Castelnuovo normality bound for smooth varieties.
Extent	60.0
Subject	Mathematics Commutative rings and algebras Algebraic geometry Algebraic structures
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: KAIST
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-03-23
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0377350
URI	http://hdl.handle.net/2429/69108
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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