Étale triviality of finite vector bundles over compact complex manifolds

Biswas, Indranil

doi:10.1016/j.aim.2020.107167

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…As mentioned above, when X is a compact complex manifold, and H = {e}, Theorem 1.1 was proved in [Bis20]. The proof of Theorem 1.1 given here is an application of the splitting theorem of [AK02], [O'S05] and [O'S19].…”

Section: Introductionmentioning

confidence: 82%

“…We recall that astheno-Kähler metrics, introduced in [JY93], are weaker than Kähler metrics. More recently, in [Bis20] this result was proved for holomorphic vector bundles over any compact complex manifold.…”

Section: Introductionmentioning

confidence: 92%

“…The proof of Theorem 1.1 given here is an application of the splitting theorem of [AK02], [O'S05] and [O'S19]. It is simpler and much shorter than the proof given in [Bis20]. It resembles [And09] in the sense that it constitutes a simple category theoretic proof of a result proved using elaborate analytical methods.…”

Section: Introductionmentioning

confidence: 95%

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\'Etale triviality of finite equivariant vector bundles

Biswas¹,

O’Sullivan²

2021

Épijournal De Géométrie Algébrique

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Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle E over X is $H$-finite, meaning f_1(E)= f_2(E) as H-equivariant bundles for two distinct polynomials f_1 and f_2 whose coefficients are nonnegative integers, if and only if the pullback of E along some H-equivariant finite \'etale covering of X is trivial as an H-equivariant bundle.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 92%

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\'Etale triviality of finite equivariant vector bundles

Biswas¹,

O’Sullivan²

2021

Épijournal De Géométrie Algébrique

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Holomorphic Bundles Trivializable by Proper Surjective Holomorphic Map

Biswas

Dumitrescu

2020

International Mathematics Research Notices

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Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $\varphi ^* E$ is holomorphically trivial for some surjective holomorphic map $\varphi $, to $M$, from some compact complex manifold. We prove that these are exactly those holomorphic vector bundles that admit a flat holomorphic connection with finite monodromy homomorphism. A similar result is proved for holomorphic principal $G$-bundles, where $G$ is a connected reductive complex affine algebraic group.

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Stability of symmetric powers of vector bundles of rank two with even degree on a curve

Kim

2021

Int. J. Math.

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This paper treats the strict semi-stability of the symmetric powers [Formula: see text] of a stable vector bundle [Formula: see text] of rank [Formula: see text] with even degree on a smooth projective curve [Formula: see text] of genus [Formula: see text]. The strict semi-stability of [Formula: see text] is equivalent to the orthogonality of [Formula: see text] or the existence of a bisection on the ruled surface [Formula: see text] whose self-intersection number is zero. A relation between the two interpretations is investigated in this paper through elementary transformations. This paper also gives a classification of [Formula: see text] with strictly semi-stable [Formula: see text]. Moreover, it is shown that when [Formula: see text] is stable, every symmetric power [Formula: see text] is stable for all but a finite number of [Formula: see text] in the moduli of stable vector bundles of rank [Formula: see text] with fixed determinant of even degree on [Formula: see text].

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Étale triviality of finite vector bundles over compact complex manifolds

Cited by 5 publications

References 13 publications

\'Etale triviality of finite equivariant vector bundles

\'Etale triviality of finite equivariant vector bundles

Holomorphic Bundles Trivializable by Proper Surjective Holomorphic Map

Stability of symmetric powers of vector bundles of rank two with even degree on a curve

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