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I am a maître de conférences at the Laboratoire de Mathématiques de Bretagne Atlantique of the Université de Bretagne Occidentale in Brest.
Previously, I was a a Marie Skłodowska-Curie postdoctoral fellow at the Institut Camille Jordan (Université Lyon 1), working on the project CR-Yamabe problem, Kähler metrics and K-stability with Eveline Legendre. I have also worked in the CIRGET laboratory of UQAM with Julien Keller and at SISSA and IGAP with Jacopo Stoppa.
You can find a brief CV (not always up to date) here.
Primary email address: carlo.scarpa@univ-brest.fr.
My research focus is on Kähler geometry, particularly on the existence of Kähler metrics with special curvature properties, such as (in increasing generality) Kähler-Einstein metrics, constant scalar curvature (cscK) metrics or extremal Kähler metrics.
For an introduction to these topics I recommend this book by Gábor Székelyhidi, Paul Gauduchon's book, and two papers by Richard Thomas and Julius Ross and Ruadhaí Dervan.
I am mainly interested in problems where the existence of metrics with special curvature properties is coupled with other aspects of the theory of complex manifolds, like the study of deformations of complex structures.
Students:
Students:
Pietro Ciusa, PhD student at SISSA. Co-supervision with Jacopo Stoppa
Research
Research
All my works can be found on the arXiv.
Papers and preprints
Papers and preprints
The toric CR Yamabe problem, with Christina Tønnesen-Friedman and Eveline Legendre. preprint arXiv:2607.27441 [math.DG]
A K-energy functional for complexified Kähler classes. Documenta Mathematica 31 (2026), no. 5. https://doi.org/10.4171/dm/1090
Yamabe-type problems on compact Hermitian manifolds, with Daniele Angella, Francesco Pediconi, Cristiano Spotti, Oluwagbenga Joshua Windare. preprint arXiv:2605.31028[math.DG]
Z-critical equations for holomorphic vector bundles on Kähler surfaces, with Julien Keller. Mathematische Annalen 395, 10 (2026). https://doi.org/10.1007/s00208-026-03441-5
The CR Yamabe invariant and constant scalar curvature Sasaki metrics, with Abdellah Lahdili and Eveline Legendre. preprint arXiv:2509.00743[math.DG]
Polynomial stability conditions for vector bundles: positivity, equivariance and blow-ups, with Rémi Delloque, Achim Napame and Carl Tipler. preprint arXiv:2506.23842 [math.AG]. Revista Matemática Complutense, to appear
Special representatives of complexified Kähler classes, with Jacopo Stoppa. Selecta Mathematica 30, 64 (2024), https://doi.org/10.1007/s00029-024-00955-1
The Einstein-Hilbert functional and the Donaldson-Futaki invariant, with Abdellah Lahdili and Eveline Legendre. preprint arXiv:2310.11625[math.DG]. Mathematische Annalen, to appear
Scalar curvature and deformations of complex structures. Journal für die reine und angewandte Mathematik (Crelles Journal) 797, 255-283 (2023), https://doi.org/10.1515/crelle-2023-0010
The HcscK system in symplectic coordinates, with Jacopo Stoppa. Mathematische Zeitschrift 301, 75–113 (2022), https://doi.org/10.1007/s00209-021-02902-8
Solutions to Donaldson’s hyperkähler reduction on a curve, with Jacopo Stoppa. Journal of Geometric Analysis 31, 2871–2889 (2021), https://doi.org/10.1007/s12220-020-00377-3
Scalar curvature and an infinite-dimensional hyperkähler reduction, with Jacopo Stoppa. Asian Journal of Mathematics, Vol 24, N. 4, 671–724 (2020), https://dx.doi.org/10.4310/AJM.2020.v24.n4.a7
My thesis:
My thesis:
The Hitchin-cscK system: an infinite-dimensional hyperkähler reduction
Miscellaneous:
Miscellaneous:
a recording of a talk on the paper The Einstein-Hilbert functional and the Donaldson-Futaki invariant: link
together with Eveline Legendre and Rémi Reboulet, I have organised a workshop on Kähler and non-Archimedean Geometry in Lyon in November 2024. You can find more information on the conference website.
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