Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.05620 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910615378853888 |
|---|---|
| author | Collins, Tristan C. Lo, Jason Shi, Yun Yau, Shing-Tung |
| author_facet | Collins, Tristan C. Lo, Jason Shi, Yun Yau, Shing-Tung |
| contents | We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $ω$ an ample class such that $ω$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $ωc_1(L)>0$, the twisted ampleness of $L$ respect to $ω$, always implies the $σ_{ω, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau for a class of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces Collins, Tristan C. Lo, Jason Shi, Yun Yau, Shing-Tung Algebraic Geometry We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $ω$ an ample class such that $ω$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $ωc_1(L)>0$, the twisted ampleness of $L$ respect to $ω$, always implies the $σ_{ω, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau for a class of examples. |
| title | Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2306.05620 |