Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
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B N Suhas
und
Amit Kumar Singh
Abstract
Let C be a comb-like curve over ℂ and let E be a vector bundle of rank n on C. In this paper, we investigate the criteria for the semistability of the restriction of E onto the components of C when E is given to be semistable with respect to a polarization w. As an application, assuming that each irreducible component of C is general in its moduli space, we investigate the w-semistability of kernel bundles on such curves, extending the results (completely for rank two and partially for higher rank) known in the case of a reducible nodal curve with two smooth components, but here using different techniques.
Funding statement: The first and the third author were partially supported by a grant from Infosys Foundation. The third author was supported by the National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Government of India (0204/2/2022/R&D-II/1785).
Acknowledgements
We thank the referee for carefully reading the article and for all the suggestions which have improved the overall quality of the article.
Communicated by: R. Cavalieri
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Artikel in diesem Heft
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
Artikel in diesem Heft
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
