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000175897 024 7_ $2 doi $a 10.4310/CAG.2017.v25.n1.a4
000175897 024 8_ $9 scholar $9 driver $9 artpubuab $a oai:ddd.uab.cat:175897
000175897 035 __ $9 recercauab $a ARE-81494
000175897 035 __ $9 scopus_id $a 85021168656
000175897 035 __ $9 wos_id $a 000403105200004
000175897 035 __ $a oai:egreta.uab.cat:publications/a76a1106-3386-433b-bb73-9283d41fb940
000175897 041 0_ $a eng
000175897 100 1_ $a Dumnicki, Marcin
000175897 245 1_ $a Very general monomial valuations of P2 and a Nagata type conjecture
000175897 251 __ $1 http://purl.org/coar/version/c_970fb48d4fbd8a85 $2 openaire4 $9 VoR $a Versió publicada
000175897 260 __ $c 2017
000175897 500 __ $a Agraïments: This research was supported through the programme "Research in Pairs" by the Mathematisches Forschungsinstitut Oberwolfach in 2013. Alex Küronya was partially supported by the DFG-Forschergruppe 790 "Classification of Algebraic Surfaces and Compact Complex Manifolds", by the DFG-Graduiertenkolleg 1821 "Cohomological Methods in Geometry", and by the OTKA grants 77476 and 81203 of the Hungarian Academy of Sciences. Brian Harbourne's work on this project was partially sponsored by the National Security Agency under Grant/Cooperative agreement "Advances on Fat Points and Symbolic Powers," Number H98230-11-1-0139. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notice.
000175897 520 3_ $a It is well known that multi-point Seshadri constants for a small number t of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for t≥9 points. Tackling the problem in the language of valuations one can make sense of t points for any real t≥1. We show somewhat surprisingly that a Nagata-type conjecture should be valid for t≥8+1/36 points and we compute explicitly all Seshadri constants (expressed here as the asymptotic maximal vanishing element) for t≤7+1/9. In the range 7+1/9≤t≤8+1/36 we are able to compute some sporadic values.
000175897 536 __ $a Ministerio de Economía y Competitividad $d https://doi.org/10.13039/501100003329 $f MTM2013-40680-P
000175897 540 __ $9 open access $a Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets. $u https://rightsstatements.org/vocab/InC/1.0/
000175897 546 __ $a Anglès
000175897 599 __ $a recerca
000175897 653 1_ $a Nagata conjecture
000175897 653 1_ $a SHGH conjecture
000175897 653 1_ $a Seshadri constants
000175897 653 1_ $a Monomial valuations
000175897 653 1_ $a Anticanonical divisor
000175897 655 _7 $1 http://purl.org/coar/resource_type/c_6501 $2 openaire4 $a Article $c literature
000175897 700 1_ $a Küronya, Alex
000175897 700 1_ $0 0000-0002-8692-3919 $a Harbourne, Brian
000175897 700 1_ $0 0000-0003-0033-8442 $a Roé Vellvé, Joaquim $u Universitat Autònoma de Barcelona. Departament de Matemàtiques
000175897 700 1_ $0 0000-0002-4234-5838 $a Szemberg, Tomasz
000175897 773 __ $g Vol 25 núm 1 (2017), p. 125-161 $t Communications in Analysis and Geometry $x 1019-8385
000175897 856 40 $p 28 $s 400622 $u https://ddd.uab.cat/pub/artpub/2017/175897/ValNagata.pdf $z Post-print
000175897 973 __ $x 1019-8385_a2017 $y 2017
000175897 980 __ $a ARTPUB $b UAB