Let be a normal toric variety over a perfect field and let be its space of arcs. Let be a toric stable point of , i.e. defined by a toric divisorial valuation . We describe the irreducible components of and their respective dimensions. This description is derived from the existence of a finite family of regular toric varieties such that every wedge centered at lifts to some of them. As a first consequence, we obtain that, in general, the ring is neither analytically irreducible nor catenary. A second consequence is that, when is -Gorenstein, we recover the log discrepancy of from the space of arcs .
Soit une variété torique normale sur un corps parfait et soit son espace d’arcs. Soit un point stable torique de , i.e. défini par une valuation divisorielle torique . Nous décrivons les composantes irréductibles de et leur dimension respective. Cette description est déduite de l’existence d’une famille finie de variétés toriques régulières telles que tout coin centré en se relève à l’une d’elles. Comme première conséquence, nous obtenons que l’anneau n’est ni analytiquement irréductible ni caténaire en général. Une deuxième conséquence est que, lorsque est -Gorenstein, nous récupérons la log-discrépance de à partir de l’espace d’arcs .
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Keywords: Space of arcs, divisorial valuation, toric variety.
Mot clés : Espace d’arcs, valuation divisorielle, variété torique.
Reguera, Ana J. 1
@article{AIF_2023__73_5_2135_0, author = {Reguera, Ana J.}, title = {Arc spaces and wedge spaces for toric varieties}, journal = {Annales de l'Institut Fourier}, pages = {2135--2183}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {5}, year = {2023}, doi = {10.5802/aif.3568}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3568/} }
TY - JOUR AU - Reguera, Ana J. TI - Arc spaces and wedge spaces for toric varieties JO - Annales de l'Institut Fourier PY - 2023 SP - 2135 EP - 2183 VL - 73 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3568/ DO - 10.5802/aif.3568 LA - en ID - AIF_2023__73_5_2135_0 ER -
%0 Journal Article %A Reguera, Ana J. %T Arc spaces and wedge spaces for toric varieties %J Annales de l'Institut Fourier %D 2023 %P 2135-2183 %V 73 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3568/ %R 10.5802/aif.3568 %G en %F AIF_2023__73_5_2135_0
Reguera, Ana J. Arc spaces and wedge spaces for toric varieties. Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 2135-2183. doi : 10.5802/aif.3568. https://aif.centre-mersenne.org/articles/10.5802/aif.3568/
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