Author:
Barban Lorenzo,Franceschini Alberto
Abstract
AbstractWe 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 $$\mathbb {P}^1\times \mathbb {P}^1$$
P
1
×
P
1
and by $$\mathbb {P}\left( T_{\mathbb {P}^2}\right) $$
P
T
P
2
. Using the Morelli-Włodarczyk cobordism, we prove that any smooth projective variety of Picard number 1, endowed with a $${\mathbb C}^*$$
C
∗
-action with only two fixed point components, induces a rooftop flip.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
Reference22 articles.
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