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Arnold's Trivium
1991 Arnold's Trivium
43
Problem 43
Problem 43
Source:
July 1, 2010
Problem Statement
Find the Betti numbers of the surface
x
1
2
+
⋯
+
x
k
2
−
y
1
2
−
⋯
−
y
l
2
=
1
x_1^2+\cdots+x_k^2-y_1^2-\cdots-y_l^2=1
x
1
2
+
⋯
+
x
k
2
−
y
1
2
−
⋯
−
y
l
2
=
1
and the set
x
1
2
+
⋯
+
x
k
2
≤
1
+
y
1
2
+
⋯
+
y
l
2
x_1^2+\cdots+x_k^2\le1+y_1^2+\cdots+y_l^2
x
1
2
+
⋯
+
x
k
2
≤
1
+
y
1
2
+
⋯
+
y
l
2
in a
(
k
+
l
)
(k+l)
(
k
+
l
)
-dimensional linear space.
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