# Contractions of affine spherical varieties

## Abstract

The language of filtrations and contractions is used to describe the class of G-varieties obtainable as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory. These varieties are local models for arbitrary affine G-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups and three-dimensional SL{sub 2}-varieties are considered.

- Authors:

- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202880

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 190; Journal Issue: 7; Other Information: DOI: 10.1070/SM1999v190n07ABEH000413; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTRACTION; FILTRATION; MATHEMATICAL SPACE; ONE-DIMENSIONAL CALCULATIONS; SPHERICAL CONFIGURATION; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Arzhantsev, I V.
```*Contractions of affine spherical varieties*. United States: N. p., 1999.
Web. doi:10.1070/SM1999V190N07ABEH000413; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Arzhantsev, I V.
```*Contractions of affine spherical varieties*. United States. doi:10.1070/SM1999V190N07ABEH000413; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Arzhantsev, I V. Tue .
"Contractions of affine spherical varieties". United States. doi:10.1070/SM1999V190N07ABEH000413; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202880,
```

title = {Contractions of affine spherical varieties},

author = {Arzhantsev, I V},

abstractNote = {The language of filtrations and contractions is used to describe the class of G-varieties obtainable as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory. These varieties are local models for arbitrary affine G-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups and three-dimensional SL{sub 2}-varieties are considered.},

doi = {10.1070/SM1999V190N07ABEH000413; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 7,

volume = 190,

place = {United States},

year = {1999},

month = {8}

}

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