# Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

Edoardo Ballico; Francesco Malaspina

Open Mathematics (2008)

- Volume: 6, Issue: 1, page 143-148
- ISSN: 2391-5455

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topEdoardo Ballico, and Francesco Malaspina. "Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology." Open Mathematics 6.1 (2008): 143-148. <http://eudml.org/doc/269182>.

@article{EdoardoBallico2008,

abstract = {Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = \[ \mathcal \{O\} \]
Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.},

author = {Edoardo Ballico, Francesco Malaspina},

journal = {Open Mathematics},

keywords = {Hirzebruch surface; vector bundle; natural cohomology},

language = {eng},

number = {1},

pages = {143-148},

title = {Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology},

url = {http://eudml.org/doc/269182},

volume = {6},

year = {2008},

}

TY - JOUR

AU - Edoardo Ballico

AU - Francesco Malaspina

TI - Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

JO - Open Mathematics

PY - 2008

VL - 6

IS - 1

SP - 143

EP - 148

AB - Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = \[ \mathcal {O} \]
Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.

LA - eng

KW - Hirzebruch surface; vector bundle; natural cohomology

UR - http://eudml.org/doc/269182

ER -

## References

top- [1] Catanese F., Footnotes to a theorem of Reider, In: Sommese A.J., Biancofiore A., Livorni E.L. (Eds.), Algebraic Geometry Proceedings(L’Aquila 1988), Lecture Notesin Math. 1417, Springer, Berlin, 1990, 67–74 http://dx.doi.org/10.1007/BFb0083333
- [2] Fogarty J., Algebraic families on analgebraic surface, Amer. J. Math., 1968, 90, 511–521 http://dx.doi.org/10.2307/2373541 Zbl0176.18401
- [3] Hartshorne R., Stable reflexive sheaves, Math. Ann., 1980, 254, 121–176 http://dx.doi.org/10.1007/BF01467074 Zbl0431.14004
- [4] Huybrechts D., Lehn M., The geometry of moduli spaces of sheaves, Friedr. Vieweg & Sohn, Braunschweig, 1997 Zbl0872.14002

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