Alpha-invariants and purely log terminal blow-ups

We prove that the sum of the $\alpha$-invariants of two different Koll\'ar components of a Kawamata log terminal singularity is less than $1$.Comment: 12 page

QUARTIC DOUBLE SOLIDS WITH ICOSAHEDRAL SYMMETRY

We study quartic double solids admitting icosahedral symmetry.Comment: 19 page

Total log canonical thresholds and generalized Eckardt points

Let X be a smooth hypersurface of degree n greater than or equal to 3 in P-n. It is proved that the log canonical threshold of an arbitrary hyperplane section H of it-is at least (n - 1)/n. Under the assumption of the log minimal model program it is also proved that the log canonical threshold of H subset of X is (n - 1)/n if and only if H is a cone in Pn-1 over a smooth hypersurface of degree n in Pn-2.X1110sciescopu