Metric Dependence and Asymptotic Minimization of the Expected Number of Critical Points of Random Holomorphic Sections
| dc.creator | Baugher, Benjamin | |
| dc.date | 2008-02-12 | |
| dc.date | 2008-02-18 | |
| dc.date.accessioned | 2026-07-07T09:21:08Z | |
| dc.date.available | 2026-07-07T09:21:08Z | |
| dc.description | We prove the main conjecture from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the metric dependence and asymptotic minimization of the expected number \mathcal{N}^{crit}_{N,h} of critical points of random holomorphic sections of the Nth tensor power of a positive line bundle. The first non-topological term in the asymptotic expansion of \mathcal{N}^{crit}_{N,h} is the the Calabi functional multiplied by the constant \be_2(m) which depends only on the dimension of the manifold. We prove that \be_2(m) is strictly positive in all dimensions, showing that the expansion is non-topological for all m, and that the Calabi extremal metric, when it exists, asymptotically minimizes \mathcal{N}^{crit}_{N,h}. | |
| dc.description | 19 pages, added references; also includes a Mathematica worksheet in both notebook and pdf form | |
| dc.identifier | https://arxiv.org/abs/0802.1549 | |
| dc.identifier | http://arxiv.org/abs/0802.1549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154915 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Metric Dependence and Asymptotic Minimization of the Expected Number of Critical Points of Random Holomorphic Sections | |
| dc.type | text |