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Manin's conjecture for a bi-projective variety Heath-Brown, Roger
Description
This is joint work with Tim Browning. The talk concerns the variety $X_1Y_1^2+X_2Y_2^2+X_3Y_3^2+X_4Y_4^2=0$ in $P^3 \times P^3$. The height of a point $(x,y)$ is given by $H(x)^3H(y)^2$, and Manin's conjecture predicts asymptotically $cB \log B$ points of height at most $B$. To obtain this one must exclude points on the subvariety $x_1x_2x_3x_4=0$; but in order to achieve the Peyre constant one must exclude an infinite number of subvarieties in which $x_1x_2x_3x_4$ is a square. By combining the circle method with lattice point counting techniques we are able to prove Manin's conjecture for this example, and the talk will give an overview of the various ingredients, and the way that they fit together.
Item Metadata
Title |
Manin's conjecture for a bi-projective variety
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-31T09:00
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Description |
This is joint work with Tim Browning. The talk concerns the variety $X_1Y_1^2+X_2Y_2^2+X_3Y_3^2+X_4Y_4^2=0$ in $P^3 \times P^3$. The height of a point $(x,y)$ is given by $H(x)^3H(y)^2$, and Manin's conjecture predicts asymptotically $cB \log B$ points of height at most $B$. To obtain this one must exclude points on the subvariety $x_1x_2x_3x_4=0$; but in order to achieve the Peyre constant one must exclude an infinite number of subvarieties in which $x_1x_2x_3x_4$ is a square.
By combining the circle method with lattice point counting techniques we are able to prove Manin's conjecture for this example, and the talk will give an overview of the various ingredients, and the way that they fit together.
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Extent |
59.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Oxford University
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Series | |
Date Available |
2019-03-14
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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 |
10.14288/1.0376871
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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