Discrete Equivalence of Non-positive at Infinity Plane Valuations

Galindo, Carlos; Monserrat, Francisco; Moreno-Ávila, Carlos-Jesús

doi:10.1007/s00025-021-01435-0

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Notice That the Affine Open Sets1

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Cited by 2 publications

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“…We are only interested in a particular type of special divisorial valuations of F δ which was introduced in [16, Definition 3.5]. As we will see in the forthcoming Theorem 2.3, these valuations give rise to rational surfaces with nice geometrical properties (see also [17]). Let us recall the definition; set F 1 the fiber of the projection morphism F δ → P 1 that goes through p.…”

Section: Notice That the Affine Open Setsmentioning

confidence: 99%

On the Degree of Curves with Prescribed Multiplicities and Bounded Negativity

Galindo

Monserrat

Moreno-Ávila

et al. 2022

International Mathematics Research Notices

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We provide a lower bound on the degree of curves of the projective plane $\mathbb {P}^2$ passing through the centers of a divisorial valuation $\nu $ of $\mathbb {P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type constant of $\nu $, $\hat {\mu }(\nu )$, constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model.

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Section: Notice That the Affine Open Setsmentioning

confidence: 99%

On the Degree of Curves with Prescribed Multiplicities and Bounded Negativity

Galindo

Monserrat

Moreno-Ávila

et al. 2022

International Mathematics Research Notices

Self Cite

View full text Add to dashboard Cite

show abstract

On the degree of curves with prescribed multiplicities and bounded negativity

Galindo¹,

Monserrat²,

Moreno-Ávila³

et al. 2021

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We provide a lower bound on the degree of curves of the projective plane P 2 passing through the centers of a divisorial valuation ν of P 2 with prescribed multiplicities, and an upper bound for the Seshadri-type constant of ν, μ(ν), constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model.

show abstract

Discrete Equivalence of Non-positive at Infinity Plane Valuations

Cited by 2 publications

References 26 publications

On the Degree of Curves with Prescribed Multiplicities and Bounded Negativity

On the Degree of Curves with Prescribed Multiplicities and Bounded Negativity

On the degree of curves with prescribed multiplicities and bounded negativity

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