Exceptional collections on certain Hassett spaces
Épijournal de Géométrie Algébrique, Tome 4 (2020)
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We construct an $S_2\times S_n$ invariant full exceptional collection on Hassett spaces of weighted stable rational curves with $n+2$ markings and weights $(\frac{1}{2}+\eta, \frac{1}{2}+\eta,\epsilon,\ldots,\epsilon)$, for $0<\epsilon, \eta\ll1$ and can be identified with symmetric GIT quotients of $(\mathbb{P}^1)^n$ by the diagonal action of $\mathbb{G}_m$ when $n$ is odd, and their Kirwan desingularization when $n$ is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full $S_n$-invariant exceptional collection on $\overline{\mathcal{M}}_{0,n}$. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev-Manin spaces.
@article{10_46298_epiga_2021_volume4_6456,
author = {Castravet, Ana-Maria and Tevelev, Jenia},
title = {Exceptional collections on certain {Hassett} spaces},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {4},
year = {2020},
doi = {10.46298/epiga.2021.volume4.6456},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.volume4.6456/}
}
TY - JOUR AU - Castravet, Ana-Maria AU - Tevelev, Jenia TI - Exceptional collections on certain Hassett spaces JO - Épijournal de Géométrie Algébrique PY - 2020 VL - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.volume4.6456/ DO - 10.46298/epiga.2021.volume4.6456 LA - en ID - 10_46298_epiga_2021_volume4_6456 ER -
%0 Journal Article %A Castravet, Ana-Maria %A Tevelev, Jenia %T Exceptional collections on certain Hassett spaces %J Épijournal de Géométrie Algébrique %D 2020 %V 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.volume4.6456/ %R 10.46298/epiga.2021.volume4.6456 %G en %F 10_46298_epiga_2021_volume4_6456
Castravet, Ana-Maria; Tevelev, Jenia. Exceptional collections on certain Hassett spaces. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2021.volume4.6456
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