Integral cohomology of quotients via toric geometry
Épijournal de Géométrie Algébrique, Tome 6 (2022)
Voir la notice de l'article provenant de la source Episciences
We describe the integral cohomology of $X/G$ where $X$ is a compact complex manifold and $G$ a cyclic group of prime order with only isolated fixed points. As a preliminary step, we investigate the integral cohomology of toric blow-ups of quotients of $\mathbb{C}^n$. We also provide necessary and sufficient conditions for the spectral sequence of equivariant cohomology of $(X,G)$ to degenerate at the second page. As an application, we compute the Beauville–Bogomolov form of $X/G$ when $X$ is a Hilbert scheme of points on a K3 surface and $G$ a symplectic automorphism group of orders 5 or 7.
@article{10_46298_epiga_2022_volume6_5762,
author = {Menet, Gr\'egoire},
title = {Integral cohomology of quotients via toric geometry},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {6},
year = {2022},
doi = {10.46298/epiga.2022.volume6.5762},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.volume6.5762/}
}
TY - JOUR AU - Menet, Grégoire TI - Integral cohomology of quotients via toric geometry JO - Épijournal de Géométrie Algébrique PY - 2022 VL - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.volume6.5762/ DO - 10.46298/epiga.2022.volume6.5762 LA - en ID - 10_46298_epiga_2022_volume6_5762 ER -
%0 Journal Article %A Menet, Grégoire %T Integral cohomology of quotients via toric geometry %J Épijournal de Géométrie Algébrique %D 2022 %V 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.volume6.5762/ %R 10.46298/epiga.2022.volume6.5762 %G en %F 10_46298_epiga_2022_volume6_5762
Menet, Grégoire. Integral cohomology of quotients via toric geometry. Épijournal de Géométrie Algébrique, Tome 6 (2022). doi: 10.46298/epiga.2022.volume6.5762
Cité par Sources :