# Versal deformations and local Hilbert schemes

@article{Ilten2012VersalDA, title={Versal deformations and local Hilbert schemes}, author={Nathan Owen Ilten}, journal={arXiv: Algebraic Geometry}, year={2012}, volume={4}, pages={12-16} }

We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.

## 26 Citations

### Hilbert Schemes and Toric Degenerations for Low Degree Fano Threefolds

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For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties…

### Toric Degenerations of Low Degree Fano Threefolds

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For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties…

### SMOOTH FANO 4-FOLDS IN GORENSTEIN FORMATS

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Abstract We construct some new deformation families of four-dimensional Fano manifolds of index one in some known classes of Gorenstein formats. These families have explicit descriptions in terms of…

### The Dimension of the Moduli Space of Pointed Algebraic Curves of Low Genus

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We explicitly compute the moduli space pointed algebraic curves with a given numerical semigroup as Weierstrass semigroup for many cases of genus at most seven and determine the dimension for all…

### Families of Elliptic Curves in P3 and Bridgeland Stability

- MathematicsMichigan Mathematical Journal
- 2018

We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each of the moduli…

### Hodge numbers and deformations of Fano 3-folds

- Mathematics
- 2020

We show that index 1 Fano 3-folds which lie in weighted
Grassmannians in their total anticanonical embedding have finite automorphism group, and we relate the deformation theory of any Fano
3-fold…

### Mirror Symmetry and smoothing Gorenstein toric affine 3-folds

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We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily studied set of…

### Some Singular Lex-Segments

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We study the component structures of some standard-graded Hilbert schemes closely related to a Hilbert scheme of curves studied by Gotzmann. In particular, we encounter examples of singular…

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