Resumen de Morelli-Włodarczyk cobordism and examples of rooftop flips

Lorenzo Barban, Alberto Franceschini

• 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.