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Negative curves on ${\bf P}^2$ Harbourne, Brian
Description
Consider a plane curve of degree d with points $p_1,\ldots,p_s$ of multiplicities $m_1=mult_{p_1}(C),\ldots,m_s=mult_{p_s}(C)$. Define $Q(C,p_1,\ldots,p_s)$ to be $d^2-\sum_im_i^2$ and say that $C$ is negative curve of $Q<0$. A well known conjecture states that there are no integral plane curves $C$ with $Q(C,p_1,\ldots,p_s)<-1$ for generic points $p_i$. More generally, suppose we have points $q_1,\ldots,q_r$ in addition to the generic points $p_i$. Can there be integral negative curves $C$ with $Q(C,p_1,\ldots,p_s,q_1,\ldots,q_r)<-1$ if $mult_{p_i}(C)>0$ for some $i$ If so, what can be said about the occurrence of such curves Work of R. De Gennaro, D. Faenzi, G. Ilardi and J. Valles shows in general it can happen so the problem now is to classify such occurrences. I'll discuss some joint work with D. Cook II, J. Migliore and U. Nagel giving partial results.
Item Metadata
Title |
Negative curves on ${\bf P}^2$
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-05-15T08:56
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Description |
Consider a plane curve of degree d with points $p_1,\ldots,p_s$ of multiplicities $m_1=mult_{p_1}(C),\ldots,m_s=mult_{p_s}(C)$. Define $Q(C,p_1,\ldots,p_s)$ to be $d^2-\sum_im_i^2$ and say that $C$ is negative curve of $Q<0$.
A well known conjecture states that there are no integral plane curves $C$ with $Q(C,p_1,\ldots,p_s)<-1$ for generic points $p_i$.
More generally, suppose we have points $q_1,\ldots,q_r$ in addition to the generic points $p_i$. Can there be integral negative curves $C$ with $Q(C,p_1,\ldots,p_s,q_1,\ldots,q_r)<-1$ if $mult_{p_i}(C)>0$ for some $i$ If so, what can be said about the occurrence of such curves
Work of R. De Gennaro, D. Faenzi, G. Ilardi and J. Valles shows in general it can happen so the problem now is to classify such occurrences. I'll discuss some joint work with D. Cook II, J. Migliore and U. Nagel giving partial results.
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Extent |
56.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Nebrasca-Lincoln
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Series | |
Date Available |
2019-03-08
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0376689
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International