Orbifold K\"ahler-Einstein metrics on projective toric varieties

Lukas Braun

Orbifold K\"ahler-Einstein metrics on projective toric varieties

Algebraic Geometry 2022-11-15 v2 Differential Geometry

Authors: Lukas Braun

Abstract

In this short note, we investigate the existence of orbifold K\"ahler-Einstein metrics on toric varieties. In particular, we show that every $\mathbb{Q}$ -factorial normal projective toric variety allows an orbifold K\"ahler-Einstein metric. Moreover, we characterize the K-stability of $\mathbb{Q}$ -factorial toric pairs of Picard number one in terms of the log Cox ring and the universal orbifold cover.

Keywords

kähler metrics kähler-ricci flow and kähler-einstein metrics k-stability

Cite

@article{arxiv.2211.00404,
  title  = {Orbifold K\"ahler-Einstein metrics on projective toric varieties},
  author = {Lukas Braun},
  journal= {arXiv preprint arXiv:2211.00404},
  year   = {2022}
}

Comments

5 pages, new version: obtained a more general main statement building on results of Blum/Liu as well as an alternative convex geometric proof for these results. Comments are of course still very welcome

Orbifold K\"ahler-Einstein metrics on projective toric varieties

Abstract

Keywords

Cite

Comments

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