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<p>We study the birational geometry of hypersurfaces in products of weighted projective spaces, extending results previously established by J. C. Ottem. For most cases where these hypersurfaces are Mori dream spaces, we determine all relevant cones and characterise their birational models, along with their small <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">Q</mi> </math></EquationSource> </InlineEquation>-factorial modifications. We also provide a presentation of their Cox ring. Finally, we establish the birational form of the Kawamata–Morrison cone conjecture for terminal Calabi–Yau hypersurfaces in Gorenstein products of weighted projective spaces.</p>

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Birational geometry of hypersurfaces in products of weighted projective spaces

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Francesco Antonio Denisi

摘要

We study the birational geometry of hypersurfaces in products of weighted projective spaces, extending results previously established by J. C. Ottem. For most cases where these hypersurfaces are Mori dream spaces, we determine all relevant cones and characterise their birational models, along with their small \(\textbf{Q}\) Q -factorial modifications. We also provide a presentation of their Cox ring. Finally, we establish the birational form of the Kawamata–Morrison cone conjecture for terminal Calabi–Yau hypersurfaces in Gorenstein products of weighted projective spaces.