2023/03/28 by Lorenzo Barban, A. Franceschini, Barban, Lorenzo +1
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2303.15905
openalex publication_date 2023/03/28 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
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× ℙ1 and by ℙ(Tℙ2). Using the Morelli-Wlodarczyk 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.