Semistability and restrictions of tangent bundle to curves
| dc.creator | Biswas, Indranil | |
| dc.date | 2009-01-27 | |
| dc.date.accessioned | 2026-07-07T12:34:48Z | |
| dc.date.available | 2026-07-07T12:34:48Z | |
| dc.description | We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,φ)$, where $C$ is a compact connected Riemann surface and $φ: C\to X$ a holomorphic map, such that the pull back $φ^*TX$ is not semistable. 2. The variety $X$ admits an étale covering by an abelian variety. 3. The dimension $\dim X \leq 1$. We conjecture that all complex projective manifolds are of the above type, and prove that the following classes are among those that are of the above type. i) All $X$ with a finite fundamental group. ii) All $X$ such that there is a nonconstant morphism from the projective line to $X$. iii) All $X$ such that the canonical line bundle $K_X$ is either positive or negative or $c_1(K_X) \in H^2(X, {\mathbb Q})$ vanishes. iv) All projective surfaces. | |
| dc.description | Geometriae Dedicata (to appear) | |
| dc.identifier | https://arxiv.org/abs/0901.4161 | |
| dc.identifier | http://arxiv.org/abs/0901.4161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217565 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F05, 32L10 | |
| dc.title | Semistability and restrictions of tangent bundle to curves | |
| dc.type | text |