In algebraic geometry, a Coble surface was defined by Dolgachev & Zhang (2001) to be a smooth rational projective surface with empty anti-canonical linear system |−K| and non-empty anti-bicanonical linear system |−2K|. An example of a Coble surface is the blowing up of the projective plane at the 10 nodes of a Coble curve.[1]
References
edit- ^ Dolgachev, Igor V.; Zhang, De-Qi (2001), "Coble Rational Surfaces", American Journal of Mathematics, 123 (1), The Johns Hopkins University Press: 79–114, arXiv:math/9909135, doi:10.1353/ajm.2001.0002, ISSN 0002-9327, JSTOR 25099046, MR 182727879-114&rft.date=2001&rft_id=https://www.jstor.org/stable/25099046#id-name=JSTOR&rft_id=info:doi/10.1353/ajm.2001.0002&rft_id=info:arxiv/math/9909135&rft.issn=0002-9327&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=1827278#id-name=MR&rft.aulast=Dolgachev&rft.aufirst=Igor V.&rft.au=Zhang, De-Qi&rfr_id=info:sid/en.wikipedia.org:Coble surface" class="Z3988">