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
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• 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 \mathbb {P}^1\times \mathbb {P}^1 and by \mathbb {P}\left( T_{\mathbb {P}^2}\right) . Using the Morelli-Włodarczyk cobordism, we prove that any smooth projective variety of Picard number 1, endowed with a {\mathbb C}^* -action with only two fixed point components, induces a rooftop flip.