New slope inequalities for families of complete intersections

• Miguel Ángel Barja ^[1] ; Lidia Stoppino ^[2]
  1. [1] Universitat Politècnica de Catalunya-BarcelonaTech; Institut de Matemátiques de la UPC; CRM, Spain
  2. [2] Universitá di Pavia, Italy
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 1, 2024, págs. 327-353
• Idioma: inglés
• DOI: 10.4171/RMI/1461
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• Resumen

  • We prove f-positivity of OX(1) for arbitrary dimensional fibrations over curves f:X→B whose general fibre is a complete intersection. In the special case where the family is a global complete intersection, we prove numerical sufficient and necessary conditions for f-positivity of powers of OX(1) and for the relative canonical sheaf. From these results we also derive a Chow instability condition for the fibres of relative complete intersections in the projective bundle of a μ-unstable bundle.