Ramanujam vanishing theorem

In algebraic geometry, the Ramanujam vanishing theorem is an extension of the Kodaira vanishing theorem due to Ramanujam (1972), that in particular gives conditions for the vanishing of first cohomology groups of coherent sheaves on a surface. The Kawamata–Viehweg vanishing theorem generalizes it.

See also

• Mumford vanishing theorem

References

• Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen, 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831, MR 675204
• Ramanujam, C. P. (1972), "Remarks on the Kodaira vanishing theorem", J. Indian Math. Soc. (N.S.)1: 121–124, MR 0330164