On Mumford's construction of degenerating abelian varieties

DOI10.2748/tmj/1178224770zbMath0989.14003arXivalg-geom/9608014OpenAlexW2087503158MaRDI QIDQ1961358

Iku Nakamura, Valery Alexeev

Publication date: 17 January 2000

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9608014

zbMATH Keywords

theta divisorprincipally polarized abelian varietiescanonical degeneration

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Fibrations, degenerations in algebraic geometry (14D06) Fine and coarse moduli spaces (14D22)

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Balanced embedding of degenerating Abelian varieties, Weak point property and sections of Picard bundles on a compactified Jacobian over a nodal curve, LAGRANGIAN FIBRATIONS OF HYPERKÄHLER FOURFOLDS, Compactified Jacobians as Mumford models, Stable pair compactification of moduli of \(K3\) surfaces of degree 2, Compactification of the moduli of polarized abelian varieties and mirror symmetry, Torelli theorem for stable curves, Compactifications of moduli of elliptic K3 surfaces: stable pair and toroidal, From real affine geometry to complex geometry, Projective regular models for abelian varieties, semistable reduction, and the height pairing, The local structure of compactified Jacobians, Quantization of abelian varieties: distributional sections and the transition from Kähler to real polarizations, A Calabi-Yau threefold with Brauer group (ℤ/8ℤ)², Autoduality holds for a degenerating abelian variety, The KSBA compactification of the moduli space of \(D_{1,6}\)-polarized Enriques surfaces, Fourier-Mukai and autoduality for compactified Jacobians. I, Degenerated Calabi-Yau varieties with infinite components, moduli compactifications, and limit toroidal structures, PL DENSITY INVARIANT FOR TYPE II DEGENERATING K3 SURFACES, MODULI COMPACTIFICATION AND HYPER-KÄHLER METRIC

Cites Work

• Toroidal embeddings. I
• Toroidal compactification of Siegel spaces
• A cone of inhomogeneous second-order polynomials
• A new compactification of the Siegel space and degeneration of abelian varieties. I
• Toroidal degeneration of abelian varieties
• Complete moduli in the presence of semiabelian group action.
• Degenerate fibres and stable reduction of curves
• The Empty Sphere
• On moduli of stable quasi abelian varieties
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