RT info:eu-repo/semantics/article
T1 Minimal plane valuations
A1 Galindo, Carlos
A1 Monserrat, Francisco
A1 Moyano Fernández, Julio José
K1 Plane valuations
K1 Valoración de planos
K1 Algebra
K1 Álgebra
AB We consider the value ˆμ( ) = limm→∞ m−1a(mL), where a(mL) is the lastvalue 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 projectiveplane P2 over an algebraically closed field. This value contains, for valuations,similar information as that given by Seshadri constants for points. It is always truethat ˆμ( ) ≥ p1/vol( ) and minimal valuations are those satisfying the equality. Inthis paper, we prove that the Greuel-Lossen-Shustin Conjecture implies a variation ofthe 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) whichalso implies the original Nagata’s conjecture. We also provide infinitely many familiesof minimal very general valuations with an arbitrary number of Puiseux exponents, andan asymptotic result that can be considered as evidence in the direction of the abovementioned conjecture.
PB American Mathematical Society
SN 1534-7486
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/35952
UL http://uvadoc.uva.es/handle/10324/35952
LA eng
NO Journal of Algebraic Geometry, 2018, vol. 27. p. 751-783
NO Producción Científica
DS UVaDOC
RD 07-ago-2024