Lower Bounds for Waldschmidt Constants of Generic Lines in P3 and a Chudnovsky-Type Theorem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Marcin Dumnicki, Mohammad Zaman Fashami, Justyna Szpond, Halszka Tutaj-Gasińska

ABSTRACT

The Waldschmidt constant α^(I) of a radical ideal I in the coordinate ring of PN measures (asymptotically) the degree of a hypersurface passing through the set defined by I in PN. Nagata’s approach to the 14th Hilbert Problem was based on computing such constant for the set of points in P2. Since then, these constants drew much attention, but still there are no methods to compute them (except for trivial cases). Therefore, the research focuses on looking for accurate bounds for α^(I). In the paper, we deal with α^(s), the Waldschmidt constant for s very general lines in P3. We prove that α^(s)≥⌊2s-1⌋ holds for all s, whereas the much stronger bound α^(s)≥⌊2.5s⌋ holds for all s but s=4, 7 and 10. We also provide an algorithm which gives even better bounds for α^(s), very close to the known upper bounds, which are conjecturally equal to α^(s) for s large enough. More... »

PAGES

53

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00009-019-1328-8

DOI

http://dx.doi.org/10.1007/s00009-019-1328-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112685023


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