DongSeon Hwang — Page 2

arXiv2010

Algebraic Montgomery-Yang Problem: the non-rational case and the del Pezzo case

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with the second Betti number $b_2(S) = 1$ and with quotient singularities only has at most 3 singular points if its smooth locus $S^0$ is simply-connected. In a previous paper, we have confirmed the conjecture when $S$ has at least one non-cyclic quotient singularity. In this paper, we prove the conjecture either when $S$ is not rational or when $-K_S$ is ample.

math.AG↗

arXiv2010

Constructions of singular rational surfaces of Picard number one with ample canonical divisor

Kollár gave a series of examples of rational surfaces of Picard number $1$ with ample canonical divisor having cyclic singularities. In this paper, we construct several series of new examples in a geometric way, i.e., by blowing up several times inside a configuration of curves on the projective plane and then by contracting chains of rational curves. One series of our examples have the same singularities as Kollár's examples.

math.AG↗