Cascade structures on rational Q-homology projective planes

Venerdì 10 ottobre, alle ore 11:30,
Aula B3 a Palazzo Manfredini

Prof. DongSeon Hwang (Institute for Basic Sciences, Daejeon, Korea)

Abstract:
A normal projective surface with klt singularities is called a Q-homology projective plane if the topological second Betti number equals one. Several problems in differential topology, including the Montgomer-Yang problem and the rationality of the base of Sasaki-Einstein 5-manifolds, motivate the classification of Q-homology projective planes.
In this talk, after briefly reviewing the classification of Q-homology projective planes, we focus on the rational case. In particular, we propose a conjecture asserting that such surfaces admit a certain birational relation, called a cascade, which implies the algebraic Montgomery-Yang problem. We conclude by showing that the conjecture holds if the anticanonical divisor is ample.

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