Holomorphic symmetric differentials and a birational characterization of abelian varieties

Mistretta, Ernesto C.

doi:10.1002/mana.201900102

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Remark 4.3. In the situation of Claim 4, Claim 2 strengthens [34], in which the assumption κ 1 (X) = 0 is replaced by the assumption that Sym m (Ω 1 X ) is generated by its sections for large m. Proof. Claim2,3 are immediate consequences of Claim 1, which we now prove.…”

Section: 2mentioning

confidence: 90%

Numerical and kodaira dimensions of cotangent bundles

Campana¹

2022

Preprint

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We conjecture the equality of the numerical and Kodaira dimensions ν * 1 (X) and κ * 1 (X) for the cotangent bundle of a compact Kähler manifold X, similar to the classical case of the canonical bundle. We show it or reduce it to the classical case of the canonical bundle in some peculiar manifolds: among them, the rationally connected ones, or resolutions of varieties with klt singularities and trivial first Chern class, in which case we show that, where q ′ (X) is the maximal irregularity of a finite étale cover of X. The proof rests on the Beauville-Bogomolov decomposition, and a direct computation for smooth models of quotients A/G of complex tori by finite groups. We conjecture that these equalities hold true, much more generally, when X is 'special'. The invariant κ * 1 was already introduced and studied by Fumio Sakai in [43], the particular case of the preceding conjecture when κ * 1 (X) = −dim(X) was introduced and studied in [29].

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Section: 2mentioning

confidence: 90%

Numerical and kodaira dimensions of cotangent bundles

Campana¹

2022

Preprint

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“…Remark 4.4 In the recent works (cf. [2,[9][10][11]), we consider asymptotic base loci of vector bundles, to get positivity properties, and construct Iitaka fibrations. It would be interesting to consider restrictions of stable vector bundles to (smooth subvarieties in) their asymptotic base loci as well.…”

Section: Main Theoremmentioning

confidence: 99%

A remark on stability and restrictions of vector bundles to hypersurfaces

Mistretta

2021

Bol. Soc. Mat. Mex.

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“…In the recent works [3,14,16] the second named author considers stable base loci, augmented and restricted base loci for vector bundles. It would be interesting to compute explicitly the base loci in these cases for the unstable bundles M * L constructed above.…”

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confidence: 99%

On linear stability and syzygy stability

Castorena

Mistretta

Torres-López

2022

Abh. Math. Semin. Univ. Hambg.

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In previous works, the authors investigated the relationships between linear stability of a generated linear series |V| on a curve C, and slope stability of the syzygy vector bundle $$M_{V,L} := \ker (V \otimes \mathcal {O}_C \rightarrow L)$$ M V , L : = ker ( V ⊗ O C → L ) . In particular, the second named author and L. Stoppino conjecture that, for a complete linear system |L|, linear (semi)stability is equivalent to slope (semi)stability of $$M_{L}$$ M L . The first and third named authors proved that this conjecture holds in the two opposite cases: hyperelliptic and generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree 7.

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Holomorphic symmetric differentials and a birational characterization of abelian varieties

Cited by 3 publications

References 13 publications

Numerical and kodaira dimensions of cotangent bundles

Numerical and kodaira dimensions of cotangent bundles

A remark on stability and restrictions of vector bundles to hypersurfaces

On linear stability and syzygy stability

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