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Manin's conjecture for a bi-projective variety Heath-Brown, Roger May 31, 2018

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Title Manin's conjecture for a bi-projective variety
Creator Heath-Brown, Roger
Publisher Banff International Research Station for Mathematical Innovation and Discovery
Date Issued 2018-05-31T09:00
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.
Extent 59.0
Subject Mathematics
Number theory
Algebraic geometry
Arithmetic number theory
Geographic Location Oaxaca (Mexico : State)
Type Moving Image
FileFormat video/mp4
Language eng
Notes Author affiliation: Oxford University
Series BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Date Available 2019-03-14
Provider Vancouver : University of British Columbia Library
Rights Attribution-NonCommercial-NoDerivatives 4.0 International
DOI 10.14288/1.0376871
URI http://hdl.handle.net/2429/68705
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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48630-201805310900-HeathBrown_lrv.mp4 [ 393MB ]
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48630-1.0376871.ris

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