Invariance of plurigenera fails in positive and mixed characteristic
We construct smooth families of elliptic surface pairs with terminal singularities over a DVR of positive or mixed characteristic $(X,B)\to \mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently divisible $m>0$. In particular, this shows that invariance of all sufficiently...
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| creator | Brivio, Iacopo |
| description | We construct smooth families of elliptic surface pairs with terminal
singularities over a DVR of positive or mixed characteristic $(X,B)\to
\mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently
divisible $m>0$. In particular, this shows that invariance of all sufficiently
divisible plurigenera does not follow from the MMP and Abundance Conjectures. |
| doi_str_mv | 10.48550/arxiv.2011.10226 |
| format | Article |
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singularities over a DVR of positive or mixed characteristic $(X,B)\to
\mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently
divisible $m>0$. In particular, this shows that invariance of all sufficiently
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singularities over a DVR of positive or mixed characteristic $(X,B)\to
\mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently
divisible $m>0$. In particular, this shows that invariance of all sufficiently
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singularities over a DVR of positive or mixed characteristic $(X,B)\to
\mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently
divisible $m>0$. In particular, this shows that invariance of all sufficiently
divisible plurigenera does not follow from the MMP and Abundance Conjectures.</abstract><doi>10.48550/arxiv.2011.10226</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Algebraic Geometry |
| title | Invariance of plurigenera fails in positive and mixed characteristic |
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