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Versal Unfoldings
We introduce the notion of versal unfoldings of germs of maps—unfoldings which, up to A-equivalence, explore all nearby possibilities of deformation....
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Local models for Galois deformation rings and applications
We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois...
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Simplicity of Augmentations of Codimension 1 Germs and by Morse Functions
We study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the...
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Non-commutative deformations of simple objects in a category of perverse coherent sheaves
We define a category of perverse coherent sheaves as the abelian category corresponding to the category of modules under Bondal–Rickard equivalence...
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On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem
In this note we present variants of Kostov’s theorem on a versal deformation of a parabolic point of a complex analytic 1-dimensional vector field....
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Higher Displays Arising from Filtered de Rham–Witt Complexes
For a smooth projective scheme X over a ring R on which p is nilpotent that meets some general assumptions we prove that the crystalline cohomology...
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Deformation and Smoothing of Singularities
We give a survey on some aspects of deformations of isolated singularities. In addition to the presentation of the general theory, we report on the...
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Differentiable families of traceless matrix triples
Analysis of spectra of families of sets of matrices verifying certain properties is not simple because phenomena as singularities and bifurcations...
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Analytic semi-universal deformations in logarithmic complex geometry
We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a...
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Modular functions and resolvent problems
The link between modular functions and algebraic functions was a driving force behind the 19th century study of both. Examples include the solutions...
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Singularities of Map**s
We summarise some of the basic theory of \(\mathscr {A}\)...
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Reconstructions of the Asymptotics of an Integral Determined by a Hyperbolic Unimodal Singularity
AbstractThe asymptotic behavior of an exponential integral is studied in which the phase function has the form of a special deformation of the germ...
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Some Observations on the Dimension of Fano K-Moduli
In this short note we show the unboundedness of the dimension of the K-moduli space of n-dimensional Fano varieties, and that the dimension of the...
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Deformations and Extensions of Gorenstein Weighted Projective Spaces
We study the existence of deformations of all 14 Gorenstein weighted projective spaces...