Irreducibility of the Compactified Jacobian

Altman, Allen; Iarrobino, Anthony; Kleiman, Steven L.

doi:10.1007/978-94-010-1289-8_1

Cited by 66 publications

(140 citation statements)

References 7 publications

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“…The classα ∈ H 2 (M Dol ) has pure type (1,1). This raises the following question: what is the meaning of the weight filtration W • of H * (M B ) when viewed in H * (M Dol ) via the diffeomorphism M B M Dol coming from the non-Abelian Hodge theorem?…”

Section: )mentioning

confidence: 99%

Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

2012

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For G = GL2, PGL2, SL2 we prove that the perverse filtration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight filtration on the rational cohomology of the twisted G character variety of C when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.

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Section: )mentioning

confidence: 99%

Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

2012

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“…In particular, there is a 1-1 correspondence between lines and conics; hence n r 1,0 = n r 2,0 . The technique is standard [55]. We form the Grassmann bundle G = Gr 2 (O 2 ⊕ O(2)) of lines in the fibers of g. Note that dim(G) = 4.…”

Section: Verificationsmentioning

confidence: 99%

Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

1995

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The moduli dependence of (2, 2) superstring compactifications based on CalabiYau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg orbifolds with c = 9 whose potential is a sum of A-type singularities. Here we consider the generalization to arbitrary quasi-homogeneous singularities at c = 9. We use mirror symmetry to derive the dependence of the models on the complexified Kähler moduli and check the expansions of some topological correlation functions against explicit genus zero and genus one instanton calculations. As an important application we give examples of how non-algebraic ("twisted") deformations can be mapped to algebraic ones, hence allowing us to study the full moduli space. We also study how moduli spaces can be nested in each other, thus enabling a (singular) transition from one theory to another. Following the recent work of Greene, Morrison and Strominger we show that this corresponds to black hole condensation in type II string theories compactified on Calabi-Yau manifolds. CERN-TH-7528/956/95

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“…Since I was arbitrary Hilb" (X) is of dimension greater than or equal to n at every point. In [1] this fact was verified as follows. The Poincare sheaf M = Oy ® Os 1^ is a rank n vector bundle on H = Hilb" (S).…”

Section: Preliminaries and Notationmentioning

confidence: 70%

The compactified Jacobian

Rego¹

1980

Ann. Sci. École Norm. Sup.

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Irreducibility of the Compactified Jacobian

Cited by 66 publications

References 7 publications

Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

The compactified Jacobian

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