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D.5.5.3 BettiNumsH
Procedure from librarygoettsche.lib (see goettsche_lib).
- Usage:
- BettiNumsH(n, b); n integer, b list of non-negative integers
- Return:
- list of non-negative integers
- Purpose:
- computes the Betti numbers of the Hilbert scheme
of n points on a surface with Betti numbers b - Note:
- an empty list is returned if n<0 or b is not a list of non-negative integers
or if there are not enough Betti numbers
LIB "goettsche.lib"; ring r=0, (z), ls; // consider the projective plane P_2 with Betti numbers 1,0,1,0,1 list b=1,0,1,0,1; // get the Betti numbers of the Hilbert scheme of 3 points on P_2 print( BettiNumsH(3, b) ); ==> [1]: ==> 1 ==> [2]: ==> 0 ==> [3]: ==> 2 ==> [4]: ==> 0 ==> [5]: ==> 5 ==> [6]: ==> 0 ==> [7]: ==> 6 ==> [8]: ==> 0 ==> [9]: ==> 5 ==> [10]: ==> 0 ==> [11]: ==> 2 ==> [12]: ==> 0 ==> [13]: ==> 1 |