Minimal plane valuations
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Other documents of the author: Galindo, Carlos; Monserrat, Francisco; Moyano-Fernández, Julio José
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Minimal plane valuationsDate
2018-07Publisher
American Mathematical Society (AMS)Bibliographic citation
GALINDO, Carlos; MONSERRAT, Francisco; MOYANO-FERNÁNDEZ, Julio José. Minimal plane valuations. J. Algebraic Geom. 27 (2018), 751-783Type
info:eu-repo/semantics/articlePublisher version
http://www.ams.org/journals/jag/2018-27-04/S1056-3911-2018-00722-2/Version
info:eu-repo/semantics/submittedVersionAbstract
We consider the value u(v)=lim m->m-1 a(mL) , where a(mL) is the last value of the vanishing sequence of Hº(mL) along a divisorial or irrational valuation v centered at Op2,p ,L (respectively, P ) being a line ... [+]
We consider the value u(v)=lim m->m-1 a(mL) , where a(mL) is the last value of the vanishing sequence of Hº(mL) along a divisorial or irrational valuation v centered at Op2,p ,L (respectively, P ) being a line (respectively, a point) of the projective plane P2 over an algebraically closed field. This value contains, for valuations, similar information as that given by Seshadri constants for points. It is always true that u(v)>1/vol(v) and minimal valuations are those satisfying the equality. In this paper, we prove that the Greuel-Lossen-Shustin Conjecture implies a variation of the Nagata Conjecture involving minimal valuations (that extends the one stated in [Comm. Anal. Geom. 25 (2017), pp. 125-161] to the whole set of divisorial and irrational valuations of the projective plane) which also implies the original Nagata Conjecture. We also provide infinitely many families of minimal very general valuations with an arbitrary number of Puiseux exponents and an asymptotic result that can be considered as evidence in the direction of the above-mentioned conjecture. [-]
Investigation project
Spanish Government Ministerio de Economía, Industria y Competitividad/FEDER (grants MTM2012-36917-C03-03, MTM2015-65764-C3-2-P, and MTM2016-81735-REDT) ; Universitat Jaume I (grant P1-1B2015-02)Rights
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