Nakamaye’s theorem on complex manifolds

Abstract

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

KAWA lecture notes on the Kähler–Ricci flow

“…The proof of Theorem 4.9 is quite technical and involves very different techniques from the ones in these notes. Therefore we will skip its proof, referring the interested reader to the original article [10] or to the survey [78]. For the reader who is familiar with these concepts (see e.g.…”

Envelopes with Prescribed Singularities

“…We can now avail ourselves of Proposition 3.3. Recall the elementary fact that if θ is a Kähler form on Y with volume one, then ε y (θ) Vol(θ) 1/n = 1 for all y ∈ Y , and that we always have equality in the case when Y is a Riemann surface; see, for example, [43,Theorem 4.6], or the explicit construction in [39, Lemma 5.5]. Thus, ε τ (2ω F S ) = 2 > 1 ε z 0 (ω) for all τ ∈ D ⊂ CP 1 , and so we may apply Proposition 3.3 to see that ε (z 0 ,0) (π * ω + 2p * ω F S ) = ε z 0 (ω).…”