Hirzebruch曲面某些爆破的有效拟群

IF 0.9 Q2 MATHEMATICS Arabian Journal of Mathematics Pub Date : 2023-03-13 DOI:10.1007/s40065-023-00425-0

G. Andablo-Reyes, B. L. De La Rosa-Navarro, M. Lahyane

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引用次数: 0

摘要

我们主要给出了一个数值条件来保证某些光滑投影有理曲面的有效半群的有限生成。这些表面是由任何固定的Hirzebruch表面在一些普通点的特殊配置下的放大而成的。在这个数值条件下，我们明确地确定了所有\（（-1）\）和\（（-2）\）-曲线的列表。特别是，我们完成了Harbourne获得的一个结果（Duke Math J 52（1）：129–1481985）和第三作者获得的另一个结果，（C R Math 338（11）：873–8782004）。此外，这些曲面的Cox环是有限生成的。我们的地场被假定为具有任何特征的代数封闭的。

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The effective monoids of some blow-ups of Hirzebruch surfaces

We mainly give a numerical condition to ensure the finite generation of the effective monoids of some smooth projective rational surfaces. These surfaces are constructed from the blow-up of any fixed Hirzebruch surface at some special configurations of ordinary points. Under this numerical condition, we determine explicitly the list of all \((-1)\) and \((-2)\)-curves. In particular, we complete a result obtained by Harbourne (Duke Math J 52(1):129–148, 1985) and another result obtained by the third author (C R Math 338(11):873–878, 2004). Moreover, the Cox rings of these surfaces are finitely generated. Our ground field is assumed to be algebraically closed of any characteristic.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.