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Lefschetz properties for ideals of powers of linear forms -- old and new results Migliore, Juan
Description
Let $R$ be a polynomial ring in $r$ variables. Let $L$ be a general linear form. A result of Stanley and of Watanabe says that if I is an ideal generated by $r$ powers of linearly independent linear forms (e.g. the variables), and if $j$ and $k$ are any positive integers, then multiplication by $L^k$ from the degree $j$ component of $R/I$ to the degree $j+k$ component has maximal rank. This leads to the question of what happens when we have powers of more than $r$ linear forms. Over the last decade or so several papers have addressed different aspects of this problem, most often focusing on the case $k=1$ (i.e. studying the so-called Weak Lefschetz Property). In the last half year or so, progress has been made on the problem when $k > 1$. I will give an overview of the history of this problem, talk about recent work in collaboration with R. Miró-Roig and with U. Nagel, and mention open problems and directions for new research.
Item Metadata
Title |
Lefschetz properties for ideals of powers of linear forms -- old and new results
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-05-18T09:03
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Description |
Let $R$ be a polynomial ring in $r$ variables. Let $L$ be a general linear form. A result of Stanley and of Watanabe says that if I is an ideal generated by $r$ powers of linearly independent linear forms (e.g. the variables), and if $j$ and $k$ are any positive integers, then multiplication by $L^k$ from the degree $j$ component of $R/I$ to the degree $j+k$ component has maximal rank. This leads to the question of what happens when we have powers of more than $r$ linear forms. Over the last decade or so several papers have addressed different aspects of this problem, most often focusing on the case $k=1$ (i.e. studying the so-called Weak Lefschetz Property). In the last half year or so, progress has been made on the problem when $k > 1$. I will give an overview of the history of this problem, talk about recent work in collaboration with R. Miró-Roig and with U. Nagel, and mention open problems and directions for new research.
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Extent |
50 minutes
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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 Notre Dame
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Series | |
Date Available |
2017-11-15
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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 |
10.14288/1.0357947
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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