Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.11972 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916131130834944 |
|---|---|
| author | Ancona, Michele Gayet, Damien |
| author_facet | Ancona, Michele Gayet, Damien |
| contents | In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our lower bound is uniform, in the sense that it does not depend on $d$. We also provide uniform upper bounds for similar probabilities. These results extend to random complex curves of projective surfaces equipped with an ample line bundle. This paper can be viewed as a sequel of [1], where other metric statistics were given. On a larger time scale, it joins the general program initiated in [11] of understanding random complex hypersurfaces of projective manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How curved is a random complex curve? Ancona, Michele Gayet, Damien Algebraic Geometry Probability In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our lower bound is uniform, in the sense that it does not depend on $d$. We also provide uniform upper bounds for similar probabilities. These results extend to random complex curves of projective surfaces equipped with an ample line bundle. This paper can be viewed as a sequel of [1], where other metric statistics were given. On a larger time scale, it joins the general program initiated in [11] of understanding random complex hypersurfaces of projective manifolds. |
| title | How curved is a random complex curve? |
| topic | Algebraic Geometry Probability |
| url | https://arxiv.org/abs/2402.11972 |