Modifications Analytiques

Ancona, Vincenzo; Tomassini, Giuseppe

doi:10.1007/bfb0095882

Cited by 11 publications

(33 citation statements)

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“…where we have used Lemma 3.14 (1). Now by Lemma 3.13, the rst term on the right hand side above converges to…”

Section: By Construction We Have Connectionmentioning

confidence: 90%

“…Writing∂ A i =∂ A∞ + a i for some End E-valued (0, 1)-form a i , we have a i → 0 smoothly on U . We claim that for i suciently large there are smooth endomorphisms u i of E and a constant C such that (1)…”

Section: Ideal Hym Connections Observe From Lemma 38 That Limits a I →mentioning

confidence: 99%

“…Theorem 5.4 (Langer,[36]). Let X be a smooth projective variety, and let O X (1) be an ample line bundle on X. Let {F i } i∈S be a family of µ-(semi)stable sheaves on X with xed rank and Chern classes.…”

Section: Restriction Theoremsmentioning

confidence: 99%

“…In dimensions greater than two, semiampleness of the analogous line bundle L n−1 can be established on the weak normalisation (R µss ) wn . 1 We refer the reader to the introduction of [30] for an explanation of why the passage to the weak normalisation is necessary for technical, and very likely also philosophical, reasons. Given this, one then denes the moduli space M µss (E, J ) of slope semistable sheaves with xed determinant J , in imitation of the GIT construction, to be the projective spectrum of the ring of invariant sections of powers of L n−1 .…”

Section: Introductionmentioning

confidence: 99%

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Complex algebraic compactifications of the moduli space of Hermitian Yang–Mills connections on a projective manifold

et al. 2021

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In this paper we study the relationship between three compactications of the moduli space of gauge equivalence classes of Hermitian-Yang-Mills connections on a xed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli space of stable holomorphic vector bundles, and as such it admits an algebraic compactication by Gieseker-Maruyama semistable torsion free sheaves. A recent construction due to the rst and third authors gives another compactication as a moduli space of slope semistable sheaves. In the present article, following fundamental work of Tian generalising the analysis of Uhlenbeck and Donaldson in complex dimension two, we dene a gauge theoretic compactication by adding certain gauge equivalence classes of ideal connections at the boundary. Extending work of Jun Li in the case of bundles on algebraic surfaces, we exhibit comparison maps from the sheaf theoretic compactications and prove their continuity. The continuity, together with a delicate analysis of the bres of the map from the moduli space of slope semistable sheaves allows us to endow the gauge theoretic compactication with the structure of a complex analytic space.

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“…where we have used Lemma 3.14 (1). Now by Lemma 3.13, the rst term on the right hand side above converges to…”

Section: By Construction We Have Connectionmentioning

confidence: 90%

Section: Ideal Hym Connections Observe From Lemma 38 That Limits a I →mentioning

confidence: 99%