2021-11-30T02:59:04Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/359522021-06-24T07:40:51Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
Minimal plane valuations
Galindo, Carlos
Monserrat, Francisco
Moyano Fernández, Julio José
Plane valuations
Valoración de planos
Algebra
Álgebra
Producción Científica
We consider the value ˆμ( ) = limm→∞ m−1a(mL), where a(mL) is the last
value of the vanishing sequence of H0(mL) along a divisorial or irrational valuation
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 ˆμ( ) ≥ p1/vol( ) 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 [15]
to the whole set of divisorial and irrational valuations of the projective plane) which
also implies the original Nagata’s 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.
Ministerio de Economía, Industria y Competitividad ( grants MTM2012-36917-C03-03 / MTM2015-65764-C3-2-P / MTM2016-81735- REDT)
Universitat Jaume I (grant P1-1B2015-02)
2019-05-07T07:08:13Z
2019-05-07T07:08:13Z
2018
info:eu-repo/semantics/article
https://doi.org/10.1090/jag/722
Journal of Algebraic Geometry, 2018, vol. 27. p. 751-783
1534-7486
http://uvadoc.uva.es/handle/10324/35952
eng
http://www.ams.org/journals/jag/2018-27-04/S1056-3911-2018-00722-2/
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
© 2018 American Mathematical Society
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American Mathematical Society