2024-03-29T08:12:21Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1682892023-09-28T09:48:07Zcom_10234_7037com_10234_9col_10234_8635
Repositori UJI
author
Galindo, Carlos
author
Monserrat, Francisco
2017-07-13T09:46:10Z
2017-07-13T09:46:10Z
2016-02
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. 1040-1061
0001-8708
http://hdl.handle.net/10234/168289
https://doi.org/10.1016/j.aim.2015.12.015
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.
eng
cone of curves
Cox ring
rational surfaces
plane divisorial valuation
The cone of curves and the Cox ring of rational surfaces given by divisorial valuations
info:eu-repo/semantics/article
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2016_Galindo_Monserrat_Advances_in_Mathematics.pdf
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https://repositori.uji.es/xmlui/bitstream/10234/168289/9/2016_Galindo_Monserrat_Advances_in_Mathematics.pdf.txt
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text/plain
2016_Galindo_Monserrat_Advances_in_Mathematics.pdf.txt