%0 Generic %1 torres2020vanishing %A Torres, Sebastián %D 2020 %K GIT %T Bott vanishing using GIT and quantization %U http://arxiv.org/abs/2003.10617 %X A smooth projective variety $Y$ is said to satisfy Bott vanishing if $Ømega_Y^jL$ has no higher cohomology for every $j$ and every ample line bundle $L$. Few examples are known to satisfy this property. Among them are toric varieties, as well as the quintic del Pezzo surface, recently shown by Totaro. Here we present a new class of varieties satisfying Bott vanishing, namely stable GIT quotients of $(P^1)^n$ by the action of $PGL_2$, over an algebraically closed field of characteristic zero. For this, we use the work done by Halpern-Leistner on the derived category of a GIT quotient, and his version of the quantization theorem. We also see that, using similar techniques, we can recover Bott vanishing for the toric case.

@misc{torres2020vanishing, abstract = {A smooth projective variety $Y$ is said to satisfy Bott vanishing if $\Omega_Y^j\otimes L$ has no higher cohomology for every $j$ and every ample line bundle $L$. Few examples are known to satisfy this property. Among them are toric varieties, as well as the quintic del Pezzo surface, recently shown by Totaro. Here we present a new class of varieties satisfying Bott vanishing, namely stable GIT quotients of $(\mathbb{P}^1)^n$ by the action of $PGL_2$, over an algebraically closed field of characteristic zero. For this, we use the work done by Halpern-Leistner on the derived category of a GIT quotient, and his version of the quantization theorem. We also see that, using similar techniques, we can recover Bott vanishing for the toric case.}, added-at = {2020-05-05T09:31:16.000+0200}, author = {Torres, Sebastián}, biburl = {https://www.bibsonomy.org/bibtex/202384bf5bb477150481a545e14a6bb86/simonechiarello}, description = {Bott vanishing using GIT and quantization}, interhash = {17ff959806e6300ae3534c4a54796ec9}, intrahash = {02384bf5bb477150481a545e14a6bb86}, keywords = {GIT}, note = {cite arxiv:2003.10617Comment: submitted version}, timestamp = {2020-05-05T09:31:16.000+0200}, title = {Bott vanishing using GIT and quantization}, url = {http://arxiv.org/abs/2003.10617}, year = 2020 }