The cone of curves and the Cox ring of rational surfaces given by divisorial valuations
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Título
The cone of curves and the Cox ring of rational surfaces given by divisorial valuationsFecha de publicación
2016-02Editor
ElsevierISSN
0001-8708Cita bibliográfica
GALINDO, Carlos; MONSERRAT, Francisco. The cone of curves and the Cox ring of rational surfaces given by divisorial valuations. Advances in Mathematics, 2016, vol. 290, p. 1040-1061Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0001870815005496Versión
info:eu-repo/semantics/sumittedVersionPalabras clave / Materias
Resumen
We consider surfaces X defined by plane divisorial valuations ν of the quo-
tient field of the local ring R at a closed point p of the projective plane P
2
over an
arbitrary algebraically closed field k and ... [+]
We consider surfaces X defined by plane divisorial valuations ν of the quo-
tient field of the local ring R at a closed point p of the projective plane P
2
over an
arbitrary algebraically closed field k and centered at R. We prove that the regularity of
the cone of curves of X is equivalent to the fact that ν is non-positive on OP2 (P
2
\ L),
where L is a certain line containing p. Under these conditions, we characterize when
the characteristic cone of X is closed and its Cox ring finitely generated. Equivalent
conditions to the fact that ν is negative on OP2 (P
2
\ L) \ k are also given. [-]
Publicado en
Advances in Mathematics, v. 290, 26, February 2016, p. 1040-1061Derechos de acceso
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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