Homological Planes in the Grothendieck Ring of Varieties
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 356-362
Voir la notice de l'article provenant de la source Cambridge
In this note we identify the classes of $\text{Q}$ -homological planes in the Grothendieck group of complex varieties ${{K}_{0}}\left( \text{Va}{{\text{r}}_{\text{C}}} \right)$ . Precisely, we prove that a connected, smooth, affine, complex, algebraic surface $X$ is a $\text{Q}$ -homological plane if and only if $\left[ X \right]\,=\,\left[ \text{A}_{\text{C}}^{2} \right]$ in the ring ${{K}_{0}}\left( \text{Va}{{\text{r}}_{\text{C}}} \right)$ and $\text{Pic}{{\left( X \right)}_{\text{Q}}}\,:=\,\text{Pic}\left( X \right)\,{{\otimes }_{\text{Z}}}\,\text{Q}\,\text{=}\,\text{0}$ .
Mots-clés :
14E05, 14R10, motivic nearby cycles, motivic Milnor fiber, nearby motives
Sebag, Julien. Homological Planes in the Grothendieck Ring of Varieties. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 356-362. doi: 10.4153/CMB-2014-045-6
@article{10_4153_CMB_2014_045_6,
author = {Sebag, Julien},
title = {Homological {Planes} in the {Grothendieck} {Ring} of {Varieties}},
journal = {Canadian mathematical bulletin},
pages = {356--362},
year = {2015},
volume = {58},
number = {2},
doi = {10.4153/CMB-2014-045-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-045-6/}
}
Cité par Sources :