Degeneration of a spectral sequence

478 Views Asked by At

I am reading the book “Fourier-Mukai transforms in algebraic geometry” by Daniel Huybrechts. On page 140, he is written that due to some results the spectral sequence $$E^{p,q}_2=H^p(X\times X,\mathcal{E}xt^q(\iota_*\mathcal{O}_X,\iota_*\mathcal{O}_X))\Longrightarrow Ext^{p+q}(\iota_*\mathcal{O}_X,\iota_*\mathcal{O}_X)$$ degenerates and this implies that $$Ext^i(\iota_*\mathcal{O}_X,\iota_*\mathcal{O}_X)\cong \bigoplus_{p+q=i}H^i(X\times X, \mathcal{E}xt^q(\iota_*\mathcal{O}_X,\iota_*\mathcal{O}_X))$$ Now, my question is that what is the meaning of the degeneration of a spectral sequence and why does it imply this isomorphism here?