Murphy's law in algebraic geometry: Badly-behaved deformation spaces
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Publication:2494166
DOI10.1007/s00222-005-0481-9zbMath1095.14006arXivmath/0411469OpenAlexW1994327923MaRDI QIDQ2494166
Publication date: 16 June 2006
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0411469
Singularities in algebraic geometry (14B05) Plane and space curves (14H50) Parametrization (Chow and Hilbert schemes) (14C05) Families, moduli, classification: algebraic theory (14J10) Deformations of singularities (14B07) Local deformation theory, Artin approximation, etc. (14B12) Fine and coarse moduli spaces (14D22)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quotient spaces modulo algebraic groups
- On the moduli spaces of surfaces of general type. Appendix: Letter of E. Bombieri written to the author
- Everywhere non reduced moduli spaces
- On canonical surfaces of general type with K \(2=3_{\chi}-10\)
- D'autres composantes non réduites de Hilb\({\mathbb{P}}^ 3\). (Other non reduced components of Hilb\({\mathbb{P}}^ 3\))
- Versal deformations and algebraic stacks
- Equisingular deformations of normal surface singularities. I
- On graded rings. I
- Moduli of stable sheaves. I
- On the moduli of vector bundles on an algebraic surface
- Algebraic surfaces of general type with small \(c^2_1\). III
- Moduli of representations of the fundamental group of a smooth projective variety. I
- On the moduli space of diffeomorphic algebraic surfaces
- Projectivity of complete moduli
- Local contributions to global deformations of surfaces
- On the Hilbert scheme of curves in higher-dimensional projective space
- Diffeomorphism of simply connected algebraic surfaces
- A desingularization of the main component of the moduli space of genus-one stable maps into \(\mathbb{P}^{n}\)
- Murphy's law in algebraic geometry: Badly-behaved deformation spaces
- Arithmetic Macaulayfication of projective schemes
- Hilbert scheme components in characteristic 2
- Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic
- Genre des courbes de l'espace projectif. II
- On the Existence of Complete Families of Projective Plane Curves, which are Obstructed
- Classification of Three-Dimensional Flips
- Deformations of Plane Curves with Nodes and Cusps
- Sur le schéma de Hilbert des variétés de codimension $2$ dans $\mathbf{P}^e$ à cône de Cohen-Macaulay
- Le schéma de Hilbert des courbes gauches localement Cohen-Macaulay n'est (presque) jamais réduit
- Automorphisms and moduli spaces of varieties with ample canonical class via deformations of abelian covers
- Notes on stable maps and quantum cohomology
- ON THE NUMBER OF IRREDUCIBLE COMPONENTS OF THE HILBERT SCHEME OF SMOOTH SPACE CURVES
- On the Factoriality of Local Rings of Small Embedding Codimension
- ON OBSTRUCTIONS TO DEFORMATIONS OF COMPLEX ANALYTIC SURFACES
- Further Pathologies in Algebraic Geometry
- Abelian covers of algebraic varieties.
- Moduli of abelian varieties