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Peer-reviewedCC BY 4.0Documenta Mathematica

A K-energy functional for complexified Kähler classes

  • Carlo Scarpa
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Abstract

Given a complexified Kähler class on a compact Kähler manifold, we introduce a generalisation of the K-energy functional, defined on the space of complexified Kähler potentials, whose critical points are solutions of the scalar curvature equation with B-field introduced by Schlitzer and Stoppa. We prove that this extended K-energy is convex along geodesics in the space of almost calibrated potentials. As an application, we show that, at least in some notable cases, solutions of the scalar curvature equation with B-field are unique in their class, confirming the expectation that the scalar curvature equation with B-field identifies canonical representatives of complexified Kähler classes.

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Cite

BibTeXRIS
BibTeX
@article{scarpa2026kenergy,
  title = {{A K-energy functional for complexified Kähler classes}},
  author = {Carlo Scarpa},
  journal = {Documenta Mathematica},
  year = {2026},
  month = jul,
  doi = {10.4171/dm/1090},
  eprint = {2307.09904},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05743042v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A K-energy functional for complexified Kähler classes
AU  - Carlo Scarpa
PY  - 2026
DA  - 2026/07/08
JO  - Documenta Mathematica
DO  - 10.4171/dm/1090
UR  - https://hal.science/hal-05743042v1
AB  - Given a complexified Kähler class on a compact Kähler manifold, we introduce a generalisation of the K-energy functional, defined on the space of complexified Kähler potentials, whose critical points are solutions of the scalar curvature equation with B-field introduced by Schlitzer and Stoppa. We prove that this extended K-energy is convex along geodesics in the space of almost calibrated potentials. As an application, we show that, at least in some notable cases, solutions of the scalar curvature equation with B-field are unique in their class, confirming the expectation that the scalar curvature equation with B-field identifies canonical representatives of complexified Kähler classes.
SN  - 1431-0643
SN  - 1431-0635
ER  -