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19942026
most citedGerms of arcs on singular algebraic varieties and motivic integration

209 citations

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math.DG2024

Lower bounds on fibered Yang-Mills functionals: generic nefness and semistability of direct images

Siarhei Finski

The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarize…

math.DG2023★ 2 cited

Geometry at the infinity of the space of positive metrics: test configurations, geodesic rays and chordal distances

Siarhei Finski

From the work of Phong and Sturm in 2007, for a polarised projective manifold and an ample test configuration, one can associate the geodesic ray of plurisubharmonic metrics on the…

math.DG2022

Submultiplicative norms and filtrations on section rings

Siarhei Finski

We show that submultiplicative norms on section rings of polarised projective manifolds are asymptotically equivalent to sup-norms associated with metrics on the polarisation. We t…

math.DG2022★ 3 cited

The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds

Siarhei Finski

We study the asymptotics of the -optimal holomorphic extensions of holomorphic jets associated with high tensor powers of a positive line bundle along submanifolds. More preci…

math.DG2022

Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions

Siarhei Finski

In a setting of a complex manifold with a fixed positive line bundle and a submanifold, we consider the optimal Ohsawa-Takegoshi extension operator, sending a holomorphic section o…

math.DG2021★ 19 cited

On toric Hermitian ALF gravitational instantons

Olivier Biquard, Paul Gauduchon

We give a classification of toric, Hermitian, Ricci flat, ALF Riemannian metrics in dimension 4, including metrics with conical singularities. The only smooth examples are on one h…