Abstract
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 We consider the universal hypersurface of degree
 
 in
 
 and compute its stable cohomology (with respect to
 
). We
 describe the stable classes geometrically.
  
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              Keywords
              
                homological stability, discriminants, parameter space,
                hypersurfaces
               
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              Mathematical Subject Classification
              
                Primary: 14F25, 14J70, 55R80
               
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              Publication
              
                Received: 22 May 2021
               
              
                Revised: 11 February 2022
               
              
                Accepted: 26 February 2022
               
              
                Published: 26 September 2023
               
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