36 citations · 155 across the 22 of their papers we have counts for
23 papers
Yamabe-type problems on compact Hermitian manifolds
Daniele Angella, Francesco Pediconi, Carlo Scarpa +2
We introduce and study a one-parameter Hermitian deformation of the Yamabe problem on compact complex manifolds. The deformation is defined by adding natural torsion terms to the R…
SNC Kähler-Einstein metrics and RCD spaces
Martin de Borbon, Cristiano Spotti
We show that Kähler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact c…
On multiscale aspects of Kähler-Einstein metrics and algebraic geometry
Cristiano Spotti
We discuss how metric limits and rescalings of Kähler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singulari…
Some models for bubbling of (log) Kähler-Einstein metrics
Martin de Borbon, Cristiano Spotti
We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) Kähler-Einstein metrics in complex dimensions one and two, and further describe a conject…
A Kümmer construction for Chern-Ricci flat balanced manifolds
Federico Giusti, Cristiano Spotti
Given a non-Kähler Calabi-Yau orbifold with a finite family of isolated singularities endowed with a Chern-Ricci flat balanced metric, we show, via a gluing construction, that all…
Chern-Ricci flat balanced metrics on small resolutions of Calabi-Yau threefolds
Federico Giusti, Cristiano Spotti
Given a (smoothable) projective nodal Kähler Calabi-Yau threefold, we show, via a gluing construction, that all its - possibly non-Kähler - small resolutions admit Chern-Ricci flat…
A moment map for twisted-Hamiltonian vector fields on locally conformally Kähler manifolds
Daniele Angella, Simone Calamai, Francesco Pediconi +1
We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in Kähler Geometry to the wider framework of locally conformally Kähler Geometry.
Extremal metrics on the total space of destabilising test configurations
Lars Martin Sektnan, Cristiano Spotti
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples o…
Some observations on the dimension of Fano K-moduli
Jesus Martinez-Garcia, Cristiano Spotti
In this short note we show the unboundedness of the dimension of the K-moduli space of -dimensional Fano varieties, and that the dimension of the stack can also be unbounded whi…
Remarks on Chern-Einstein Hermitian metrics
Daniele Angella, Simone Calamai, Cristiano Spotti
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
ALE Calabi-Yau metrics with conical singularities along a compact divisor
Martin de Borbon, Cristiano Spotti
We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of with non-positive discrepancies. In particular, this incl…
Applications of the moduli continuity method to log K-stable pairs
Patricio Gallardo, Jesus Martinez-Garcia, Cristiano Spotti
The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of Kähler-Einstein metrics on Fano manifolds in some fundamental examples…
Local models for conical Kähler-Einstein metrics
Martin de Borbon, Cristiano Spotti
In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and Kähler-Einstein metrics of nega…
Calabi-Yau metrics with conical singularities along line arrangements
Martin de Borbon, Cristiano Spotti
Given a weighted line arrangement in the projective plane, with weights satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric with cone sing…
Kähler-Einstein metrics: Old and New
Daniele Angella, Cristiano Spotti
We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of…
Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
Cristiano Spotti, Song Sun
We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than tw…
Kähler-Einstein metrics on Q-smoothable Fano varieties, their moduli and some applications
Cristiano Spotti
We survey recent results on the existence of Kähler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact…
On cscK resolutions of conically singular cscK varieties
Claudio Arezzo, Cristiano Spotti
In this note we discuss the problem of resolving conically singular cscK varieties to construct smooth cscK manifolds, showing a glueing result for (some) crepant resolutions of cs…
On Chern-Yamabe problem
Daniele Angella, Simone Calamai, Cristiano Spotti
We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concer…
Existence and deformations of Kahler-Einstein metrics on smoothable Q-Fano varieties
Cristiano Spotti, Song Sun, Chengjian Yao
We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, un…
Deformations of Nodal Kähler-Einstein Del Pezzo Surfaces with Discrete Automorphism Groups
Cristiano Spotti
In this paper we prove that generic small partial smoothings of Kahler-Einstein (KE) Del Pezzo orbifolds with only nodal singularities, and with no non-zero holomorphic vector fiel…
Degenerations of Kähler-Einstein Fano Manifolds
Cristiano Spotti
In this Thesis, I investigate how Fano manifolds equipped with a Kahler-Einstein metric can degenerate as metric spaces (in the Gromov-Hausdorff topology) and some of the relations…
Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
Yuji Odaka, Cristiano Spotti, Song Sun
We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification.…