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Complex links and Hilbert-Samuel multiplicities

Abstract:

We describe a framework for estimating Hilbert–Samuel multiplicities eXY for pairs of projective varieties X⊂Y from finite point samples rather than defining equations. The first step involves proving that this multiplicity remains invariant under certain hyperplane sections which reduce X to a point p and Y to a curve C. Next, we establish that epC equals the Euler characteristic (and hence the cardinality) of the complex link of p in C. Finally, we provide explicit bounds on the number of u...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/R018472/1
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Applied Algebra and Geometry More from this journal
Volume:
7
Issue:
1
Pages:
29-48
Publication date:
2023-03-10
Acceptance date:
2022-11-10
DOI:
EISSN:
2470-6566
Language:
English
Keywords:
Pubs id:
1301063
Local pid:
pubs:1301063
Deposit date:
2022-11-10

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