Endrass surface

{{Short description|Mathematical object in algebraic geometry}} thumb|300px|right

In algebraic geometry, an '''Endrass surface''' is a nodal surface of degree 8 with 168 real nodes, found by {{harvs|txt|last=Endrass|first=Stephan|year=1997}}.<ref>{{Citation | last1=Endrass | first1=Stephan | title=A projective surface of degree eight with 168 nodes | arxiv=alg-geom/9507011 | mr=1489118 | year=1997 | journal=Journal of Algebraic Geometry | issn=1056-3911 | volume=6 | issue=2 | pages=325–334| bibcode=1995alg.geom..7011E}}</ref> This is the most real nodes known for its degree;<ref name="rla"/> however, the best proven upper bound, 174, does not match the lower bound given by this surface.<ref name="rla">{{cite book|title=Geometric Modeling and Algebraic Geometry|editor1-first=Bert|editor1-last=Jüttler|editor2-first=Ragni|editor2-last=Piene|publisher=Springer|year=2007|isbn=9783540721857|contribution=Real line arrangements and surfaces with many real nodes|pages=47–54|arxiv=math/0507234|contribution-url=https://books.google.com/books?id=1wNGq87gWykC&pg=PA47|first1=Sonja|last1=Breske|first2=Oliver|last2=Labs|first3=Duco|last3=van Straten|bibcode=2005math......7234B}}</ref><ref>{{cite journal | last = Miyaoka | first = Yoichi|authorlink= Yoichi Miyaoka | doi = 10.1007/BF01456083 | issue = 2 | journal = Mathematische Annalen | mr = 744605 | pages = 159–171 | title = The maximal number of quotient singularities on surfaces with given numerical invariants | volume = 268 | year = 1984}}</ref>

==References== {{reflist}}

Category:Algebraic surfaces