On the fattening of lines in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="bold">P</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>

Janssen, Mike

doi:10.1016/j.jpaa.2014.05.033

Cited by 6 publications

(2 citation statements)

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“…This result has already motivated a considerable amount of research, see e.g. [2], [1], [10], [15]. Whereas [10] deals still with fat points in the projective plane, [2] contains results paralleling those of [3] for P 3 and formulates a conjectural picture for higher dimensional projective spaces and higher dimensional linear subschemes of P n .…”

Section: Introductionmentioning

confidence: 99%

“…Whereas [10] deals still with fat points in the projective plane, [2] contains results paralleling those of [3] for P 3 and formulates a conjectural picture for higher dimensional projective spaces and higher dimensional linear subschemes of P n . That approach has been taken on by Jannsen [15], who studies initial degrees for ACM unions of lines in P 3 . The article [1] extends Bocci and Chiantini results from the homogeneous to the multi-homogeneous case, more precisely it deals with 0-dimensional subschemes of P 1 × P 1 .…”

Section: Introductionmentioning

confidence: 99%

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The effect of points fattening on Hirzebruch surfaces

2014

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of points fattening on Hirzebruch surfaces

2014

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Lower Bounds for Waldschmidt Constants of Generic Lines in $${\mathbb {P}}^3$$ P 3 and a Chudnovsky-Type Theorem

et al. 2019

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The Waldschmidt constant α(I) of a radical ideal I in the coordinate ring of P N measures (asymptotically) the degree of a hypersurface passing through the set defined by I in P N. Nagata's approach to the 14th Hilbert Problem was based on computing such constant for the set of points in P 2. Since then, these constants drew much attention, but still there are no methods to compute them (except for trivial cases). Therefore, the research focuses on looking for accurate bounds for α(I). In the paper, we deal with α(s), the Waldschmidt constant for s very general lines in P 3. We prove that α(s) ≥ √ 2s − 1 holds for all s, whereas the much stronger bound α(s) ≥ √ 2.5s holds for all s but s = 4, 7 and 10. We also provide an algorithm which gives even better bounds for α(s), very close to the known upper bounds, which are conjecturally equal to α(s) for s large enough.

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The Effect of Points Fattening on del Pezzo Surfaces

Lampa-Baczyńska

2020

Bull. Malays. Math. Sci. Soc.

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In this paper, we study the fattening effect of points over the complex numbers for del Pezzo surfaces $$\mathbb {S}_r$$ S r arising by blowing-up of $$\mathbb {P}^2$$ P 2 at r general points, with $$ r \in \{1, \dots , 8 \}$$ r ∈ { 1 , ⋯ , 8 } . Basic questions when studying the problem of points fattening on an arbitrary variety are what is the minimal growth of the initial sequence and how are the sets on which this minimal growth happens characterized geometrically. We provide a complete answer for del Pezzo surfaces.

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On the fattening of lines in P3

Cited by 6 publications

References 10 publications

The effect of points fattening on Hirzebruch surfaces

The effect of points fattening on Hirzebruch surfaces

Lower Bounds for Waldschmidt Constants of Generic Lines in $${\mathbb {P}}^3$$ P 3 and a Chudnovsky-Type Theorem

The Effect of Points Fattening on del Pezzo Surfaces

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