Timeline for Extending the definition of positivity from line bundles to vector bundles
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2018 at 5:54 | review | Close votes | |||
| Jan 21, 2018 at 22:40 | |||||
| Jan 21, 2018 at 5:36 | comment | added | abx | You are not the first one to ask this question, there has been a flurry of activity around this 50 years ago. Lazarsfeld's Positivity in Algebraic Geometry, II gives an excellent survey of the subject. | |
| Jan 21, 2018 at 1:40 | comment | added | Jason Starr | It is incorrect to claim that Kodaira vanishing depends only on the first Chern class. Just consider a direct sum of two holomorphic invertible sheaves on a complex projective space. If one of the two sheaves has negative degree, yet the other has positive degree such that the sum of the degrees is positive, then the first Chern class of the direct sum is positive. Yet Kodaira vanishing fails for this direct sum. | |
| Jan 21, 2018 at 1:19 | comment | added | Raymond Cheng | Given a vector bundle $V$ on a Kähler manifold $X$, call $V$ ample (or nef or...) when the (dual of the) tautological line bundle $\mathcal{O}_{\mathbf{P}(V)}(1)$ on the projectivized vector bundle $\mathbf{P}(V)$ is ample (or nef or...). See the first chapter of Lazarsfeld's "Positivity in Algebraic Geometry II" for more. For a more analytic geometric perspective, see also section 6 of Demailly's "Complex Analytic and Differential Geometry". | |
| Jan 21, 2018 at 0:55 | review | First posts | |||
| Jan 21, 2018 at 1:08 | |||||
| Jan 21, 2018 at 0:51 | history | asked | Aldo van Baerle | CC BY-SA 3.0 |