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Algebra Geometry"],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We describe a framework for estimating Hilbert\u2013Samuel multiplicities [Formula: see text] for pairs of projective varieties [Formula: see text] from finite point samples rather than defining equations. The first step involves proving that this multiplicity remains invariant under certain hyperplane sections which reduce [Formula: see text] to a point [Formula: see text] and [Formula: see text] to a curve [Formula: see text]. Next, we establish that [Formula: see text] equals the Euler characteristic (and hence the cardinality) of the complex link of [Formula: see text] in [Formula: see text]. Finally, we provide explicit bounds on the number of uniform point samples needed (in an annular neighborhood of [Formula: see text] in [Formula: see text]) to determine this Euler characteristic with high confidence.<\/jats:p>","DOI":"10.1137\/22m1475533","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T15:40:45Z","timestamp":1678376445000},"page":"29-48","source":"Crossref","is-referenced-by-count":2,"title":["Complex Links and Hilbert\u2013Samuel Multiplicities"],"prefix":"10.1137","volume":"7","author":[{"given":"Martin","family":"Helmer","sequence":"first","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vidit","family":"Nanda","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, UK, OX2 6GG."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s13163-018-0273-6"},{"key":"ref2","series-title":"Grad. 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