Bounded Negativity and Arrangements of Lines
2015 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2015, no 19, 9456-9471 p.Article in journal (Refereed) Published
The Bounded Negativity Conjecture predicts that for any smooth complex surface X there exists a lower bound for the selfintersection of reduced divisors on X. This conjecture is open. It is also not known if the existence of such a lower bound is invariant in the birational equivalence class of X. In the present note, we introduce certain constants H(X) which measure in effect the variance of the lower bounds in the birational equivalence class of X. We focus on rational surfaces and relate the value of H(ℙ^2) to certain line arrangements. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10.
Place, publisher, year, edition, pages
Oxford, England: Oxford University Press, 2015. Vol. 2015, no 19, 9456-9471 p.
Geometry Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-176639DOI: 10.1093/imrn/rnu236ISI: 000366499400011ScopusID: 2-s2.0-84950327309OAI: oai:DiVA.org:kth-176639DiVA: diva2:868115
FunderSwedish Research Council, NT:2010-5563
QC 201601142015-11-092015-11-092016-01-14Bibliographically approved