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In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
Externí odkaz:
http://arxiv.org/abs/2310.17608
Autor:
Paul, Sean Timothy
We show that the Mabuchi energy of any polarized manifold (X,L) is (bounded below) proper on the full space of Kahler metrics in the first Chern class of L if and only if (X,L) is asymptotically (semi)stable. In particular it now follows from work of
Externí odkaz:
http://arxiv.org/abs/2105.01240
Autor:
Paul, Sean Timothy
Let (X,L) be a polarized manifold. Assume that the automorphism group is finite. If the height discrepancy of (X,L) is O(d^2) then (X,L) admits a csck metric in the first chern class of L if and only if (X,L) is asymptotically stable.
Externí odkaz:
http://arxiv.org/abs/1910.06713
Autor:
Paul, Sean Timothy, Sergiou, Kyriakos
We provide an analog of the Hilbert-Chow morphism for generalized discriminants.
Externí odkaz:
http://arxiv.org/abs/1905.00086
Akademický článek
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Autor:
Paul, Sean Timothy
We show that a projective manifold is stable if and only if the Mabuchi energy is proper on the space of algebraic metrics. We show that stability implies finite automorphism group.
Comment: 28 pages. 1 Table (Appendix II). arXiv admin note: sub
Comment: 28 pages. 1 Table (Appendix II). arXiv admin note: sub
Externí odkaz:
http://arxiv.org/abs/1308.4377
Autor:
Paul, Sean Timothy
Let X be a projective manifold. We prove that the Mabuchi Energy of X is bounded below on all degenerations in B (the space of Bergman metrics) if and only if it is bounded below uniformly on B.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1210.0924
Autor:
Paul, Sean Timothy
We prove that the discriminant of a nonsingular space curve of genus $g\geq 2$ is stable with respect to the standard action of the special linear group.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/1206.6708
Autor:
Paul, Sean Timothy
We develop the connection between equivariant completions of algebraic homogeneous spaces of reductive groups and lower bounds for the Mabuchi energy of a polarized manifold over the space of Bergman metrics. We provide a new definition of Tian's CM
Externí odkaz:
http://arxiv.org/abs/1206.4923
Autor:
Paul, Sean Timothy
Let X be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of X restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n-1) and the Chow form of X. As a corollary it is shown th
Externí odkaz:
http://arxiv.org/abs/0811.2548