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We prove that a general complete intersection of dimension   n  , codimension   c   and typed  1   ,  ⋯  ,   d  cin    P  N    has ample cotangent bundle if    c  ⩾  2  n  −  2    and the degrees    d  i    are all greater than a bound that is    O  (  1  )    in   N   and quadratic in   n  . This degree bound substantially improves the currently best‐known super‐exponential bound in   N   by Deng, although our result does not address the case    n  ⩽  c  <  2  n  −  2   .

Effective bounds on ampleness of cotangent bundles