@article{7d8250fba90b4724b3322e0cd28e1d0c,
title = "Pluricomplex green's functions and fano manifolds",
abstract = "We show that if a Fano manifold does not admit K{\"a}hler-Einstein metrics then the K{\"a}hler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Amp{\`e}re equation on its complement, confirming an expectation of Tian-Yau.",
keywords = "Algebraic K{\"a}hler potentials, Fano manifold, Pluricomplex green function",
author = "Nicholas McCleerey and Valentino Tosatti",
note = "Funding Information: Acknowledgments. We thank Z. B{\l}ocki, T.C. Collins, S. Ko{\l}odziej and D.H. Phong for discussions on this topic at the AIM workshop “The complex Monge-Amp{\`e}re equation” in August 2016, E. Wulcan for her interest in this work and A. Rashkovskii and the referee for useful comments. The second-named author is also grateful to S.-T. Yau for related discussions over the years. This work was completed during the second-named author{\textquoteright}s visit to the Institut Henri Poincar{\'e} in Paris (supported by a Chaire Poincar{\'e} funded by the Clay Mathematics Institute) which he would like to thank for the hospitality and support. Funding Information: Partially supported by NSF RTG grant DMS-1502632 and by NSF grant DMS-1610278. Publisher Copyright: {\textcopyright} 2019 by the author(s).",
year = "2019",
language = "English (US)",
volume = "3",
journal = "Epijournal de Geometrie Algebrique",
issn = "2491-6765",
publisher = "Association de l'Epijournal de Geometrie Algebrique",
}