Timeline for Identifying the canonical principal polarization of a Jacobian
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2016 at 15:42 | vote | accept | Lisa S. | ||
| Mar 14, 2016 at 5:22 | comment | added | nfdc23 | The motivation for Mumford's approach is a property that doesn't refer to divisors (and so better-suited to the relative situation): inspired by the dictionary between quadratic forms and symmetric bilinear forms, Mumford's notion of polarization $f:A \rightarrow A^{\vee}$ is a map symmetric with respect to double duality such that the pullback of the Poincare bundle $P_A$ along $(1,f):A \rightarrow A \times A^{\vee}$ is ample (akin to positive-definte quadratic form). For a divisor $D$, $t_a^{\ast}(O(D))=O(t_{-a}(D))$. So the sign is caused by the language of divisors. | |
| Mar 14, 2016 at 3:33 | history | answered | abx | CC BY-SA 3.0 |