Equivalence classes of polarizations and moduli spaces of sheaves

Qin, Zhenbo

doi:10.4310/jdg/1214453682

Cited by 59 publications

(41 citation statements)

References 19 publications

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“…For nongeometric compactifications, even less is knownno one knows any analogue of the stability constraint. 4 Kahler cone substructure Note that Mumford-Takemoto stability depends implicitly upon the choice of Kahler form [2, 3,11,12,13,14,15,16,17,18,19,20]. This choice is extremely important -sheaves that are stable with respect to one Kahler form may not be stable with respect to another.…”

Section: M^) (mentioning

confidence: 99%

Kähler cone substructure

Sharpe¹

1998

Advances in Theoretical and Mathematical Physics

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To define a consistent perturbative geometric heterotic compactification the bundle is required to satisfy a subtle constraint known as "stability," which depends upon the Kahler form. This dependence upon the Kahler form is highly nontrivial -the Kahler cone splits into subcones, with a distinct moduli space of bundles in each subconeand has long been overlooked by physicists. In this article we describe this behavior and its physical manifestation.

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Section: M^) (mentioning

confidence: 99%

Kähler cone substructure

Sharpe¹

1998

Advances in Theoretical and Mathematical Physics

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“…This has been studied by a number of authors (e.g. [49], [23], [18]). Assume for simplicity that S is simply connected.…”

Section: Moduli Of Vector Bundlesmentioning

confidence: 99%

On the Motive of the Hilbert scheme of points on a surface

Göttsche

2001

Mathematical Research Letters

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The Hilbert scheme S[n] of points on an algebraic surface S is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power S (n) . For many phenomena expected for moduli spaces and nice resolutions of singular varieties it is a model case. Hilbert schemes of points have connections to several fields of mathematics, including moduli spaces of sheaves, Donaldson invariants, enumerative geometry of curves, infinite dimensional Lie algebras and vertex algebras and also to theoretical physics. This talk will try to give an overview over these connections. IntroductionThe Hilbert scheme S[n] of points on a complex projective algebraic surface S is a a parameter variety for finite subschemes of length n on S. It is a nice (crepant) resolution of singularities of the n-fold symmetric power S (n) of S. If S is a K3 surface or an abelian surface, then S[n] is a compact, holomorphic symplectic (thus hyperkähler) manifold. Thus S [n] is at the same time a basic example of a moduli space and an example of a nice resolution of singularities of a singular variety. There are a number of conjectures and general phenomena, many of which originating from theoretical physics, both about moduli spaces for objects on surfaces and about nice resolutions of singularities. In all of these the Hilbert scheme of points can be viewed as a model case and sometimes as the main motivating example. Hilbert schemes of points on a surface have connections to many topics in mathematics, including moduli spaces of sheaves and vector bundles, Donaldson invariants, Gromov-Witten invariants and enumerative geometry of curves, infinite dimensional Lie algebras and vertex algebras, noncommutative geometry and also theoretical physics.

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“…We have walls and chambers in C S in the same vein as before (actually they are the intersections of the walls and chambers of H with C S , whenever this intersection is non-empty). Now M H (c 1 , c 2 ) is constant on the chambers of C S (and so the invariant stays the same), and when H crosses a wall W ζ , M H (c 1 , c 2 ) changes (see [13]). From the point of view of the Donaldson invariants, this corresponds to restricting our attention from the positive cone of S to its ample cone.…”

Section: Introductionmentioning

confidence: 99%