On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev; Ivan Bazhov

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1713-1724
  • ISSN: 2391-5455

Abstract

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Let X be an affine toric variety. The total coordinates on X provide a canonical presentation X ¯ → X of X as a quotient of a vector space X ¯ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

How to cite

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Ivan Arzhantsev, and Ivan Bazhov. "On orbits of the automorphism group on an affine toric variety." Open Mathematics 11.10 (2013): 1713-1724. <http://eudml.org/doc/269501>.

@article{IvanArzhantsev2013,
abstract = {Let X be an affine toric variety. The total coordinates on X provide a canonical presentation \[\bar\{X\} \rightarrow X\] of X as a quotient of a vector space \[\bar\{X\}\] by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.},
author = {Ivan Arzhantsev, Ivan Bazhov},
journal = {Open Mathematics},
keywords = {Toric variety; Cox ring; Automorphism; Quotient; Luna stratification; toric variety; automorphism; quotient},
language = {eng},
number = {10},
pages = {1713-1724},
title = {On orbits of the automorphism group on an affine toric variety},
url = {http://eudml.org/doc/269501},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Ivan Arzhantsev
AU - Ivan Bazhov
TI - On orbits of the automorphism group on an affine toric variety
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1713
EP - 1724
AB - Let X be an affine toric variety. The total coordinates on X provide a canonical presentation \[\bar{X} \rightarrow X\] of X as a quotient of a vector space \[\bar{X}\] by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.
LA - eng
KW - Toric variety; Cox ring; Automorphism; Quotient; Luna stratification; toric variety; automorphism; quotient
UR - http://eudml.org/doc/269501
ER -

References

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