Morelli-Włodarczyk cobordism and examples of rooftop flips

• Barban, Lorenzo ^[1] ; Franceschini, Alberto ^[1]
  1. [1] University of Trento

     University of Trento

     Trento, Italia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 841-855
• Idioma: inglés
• DOI: 10.1007/s13348-023-00415-7
• Enlaces
  • Texto completo
• Resumen

  • We introduce the notion of rooftop flip, namely a small modification among normal projective varieties which is modeled by a smooth projective variety of Picard number 2 admitting two projective bundle structures. Examples include the Atiyah flop and the Mukai flop, modeled respectively by P1 x P1 and by P (Tp2). Using the Morelli-Włodarczyk cobordism, we prove that any smooth projective variety of Picard number 1, endowed with a C*-action with only two fixed point components, induces a rooftop flip.