Endrass surface

In algebraic geometry, an Endrass surface is a nodal surface of degree 8 with 168 real nodes, found by Stephan Endrass (1997).^[1] This is the most real nodes known for its degree;^[2] however, the best proven upper bound, 174, does not match the lower bound given by this surface.^[2]^[3]

References

^ Endrass, Stephan (1997), "A projective surface of degree eight with 168 nodes", Journal of Algebraic Geometry, 6 (2): 325–334, arXiv:alg-geom/9507011, Bibcode:1995alg.geom..7011E, ISSN 1056-3911, MR 1489118
^ ^a ^b Breske, Sonja; Labs, Oliver; van Straten, Duco (2007). "Real line arrangements and surfaces with many real nodes". In Jüttler, Bert; Piene, Ragni (eds.). Geometric Modeling and Algebraic Geometry. Springer. pp. 47–54. arXiv:math/0507234. Bibcode:2005math......7234B. ISBN 9783540721857.
^ Miyaoka, Yoichi (1984). "The maximal number of quotient singularities on surfaces with given numerical invariants". Mathematische Annalen. 268 (2): 159–171. doi:10.1007/BF01456083. MR 0744605.

[1] Endrass, Stephan (1997), "A projective surface of degree eight with 168 nodes", Journal of Algebraic Geometry, 6 (2): 325–334, arXiv:alg-geom/9507011, Bibcode:1995alg.geom..7011E, ISSN 1056-3911, MR 1489118

[rla-2] Breske, Sonja; Labs, Oliver; van Straten, Duco (2007). "Real line arrangements and surfaces with many real nodes". In Jüttler, Bert; Piene, Ragni (eds.). Geometric Modeling and Algebraic Geometry. Springer. pp. 47–54. arXiv:math/0507234. Bibcode:2005math......7234B. ISBN 9783540721857.

[3] Miyaoka, Yoichi (1984). "The maximal number of quotient singularities on surfaces with given numerical invariants". Mathematische Annalen. 268 (2): 159–171. doi:10.1007/BF01456083. MR 0744605.

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See also

References