Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar curvature and Futaki invariant of K\"ahler metrics with cone
  singularities along a divisor   We study the scalar curvature of K\"ahler metrics that have cone
singularities along a divisor, with a particular focus on certain specific
classes of such metrics that enjoy some curvature estimates. Our main result is
that, on the projective completion of a pluricanonical bundle over a product of
K\"ahler--Einstein Fano manifolds with the second Betti number 1,
momentum-constructed constant scalar curvature K\"ahler metrics with cone
singularities along the $\infty$-section exist if and only if the log Futaki
invariant vanishes on the fibrewise $\mathbb{C}^*$-action, giving a supporting
evidence to the log version of the Yau--Tian--Donaldson conjecture for general
polarisations. We also show that, for these classes of conically singular
metrics, the scalar curvature can be defined on the whole manifold as a
current, so that we can compute the log Futaki invariant with respect to them.
Finally, we prove some partial invariance results for them.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs