Holomorphic Morse Inequalities and Bergman Kernels

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Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, background): “1] by taking the twisting bundle E := X × C (in the notation of [65]) being the trivial line bundle over X, endowed with Hermitian metric | · |E := v(mφ)| · |, where | · | is the norm of C.”
Exponential estimate for the asymptotics of Bergman kernels (2013, methodology): “We refer to [15,19] for further applications of the off-diagonal expansion of the Bergman kernel to the Berezin-Toeplitz quantization, and [17] for a comprehensive study of the Bergman kernels and its applications.”
The J-flow and stability (2013, methodology): “Using the notation of [13], we apply the result to E being the trivial line bundle, with metric Λωα.”
EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS (2013, neutral): “From the L2-estimates of Hörmander (see [17] or [21]), there exists a global section τ of E ⊗ Ld such that ∂̄τ = ∂̄σ and ‖τ‖L2(hE,d ) 6 ‖∂̄σ‖L2(hE,d ) for d large enough.”