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<p>We study cones of pseudoeffective cycles on the blow up of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((\mathbb {P}^1)^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>1</mn> </msup> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> at points in very general position, proving some results concerning their structure. In particular, we show that in some cases they turn out to be generated by exceptional classes and fiber classes relatively to the projections onto a smaller number of copies of projective lines.</p>

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Cones of cycles on blowups of \((\mathbb {P}^1)^n\)

  • 期刊论文

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  • 发表日期：

    2025年3月15日

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  • Gilberto Bini,
  • Luca Ugaglia

摘要

We study cones of pseudoeffective cycles on the blow up of \((\mathbb {P}^1)^n\) ( P 1 ) n at points in very general position, proving some results concerning their structure. In particular, we show that in some cases they turn out to be generated by exceptional classes and fiber classes relatively to the projections onto a smaller number of copies of projective lines.