Dynamic alpha-invariants of del Pezzo surfaces

Abstract

For every smooth del Pezzo surface $S$, smooth curve $C\in |-K_S|$ and $\beta \in (0,1]$, we compute the $\alpha$-invariant of Tian $\alpha (S,(1-\beta )C)$ and prove the existence of Kähler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2\pi \beta$ for $\beta$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as the supremum of all $\beta \in (0,1]$ for which such a metric exists.

21 pages

References in corpus (3)

• Testing log K-stability by blowing up formalism
• Quasiplurisubharmonic Green functions
• Log canonical thresholds of Del Pezzo Surfaces in characteristic p

Cited by in corpus (2)

• Applications of the moduli continuity method to log K-stable pairs
• On the body of ample angles of asymptotically log Fano varieties