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Arnold's Trivium
1991 Arnold's Trivium
44
Problem 44
Problem 44
Source:
July 1, 2010
Problem Statement
Find the Betti numbers of the surface
x
2
+
y
2
=
1
+
z
2
x^2+y^2 = 1 + z^2
x
2
+
y
2
=
1
+
z
2
in three-dimensional projective space. The same for the surfaces
z
=
x
y
z = xy
z
=
x
y
,
z
=
x
2
z=x^2
z
=
x
2
,
z
2
=
x
2
+
y
2
z^2 = x^2 + y^2
z
2
=
x
2
+
y
2
.
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