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D.15.11 goettsche_lib

Library:
goettsche.lib
Purpose:
Goettsche's formula for the Betti numbers of the Hilbert scheme of points on a surface, Macdonald's formula for the symmetric product

Author:
Oleksandr Iena, o.g.yena@gmail.com, yena@mathematik.uni-kl.de

References:
[1] Goettsche, Lothar, The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface.
Mathematische Annalen: 286, 193-208, (1990).

[2] Macdonald, I. G., The Poincare polynomial of a symmetric product, Mathematical proceedings of the Cambridge Philosophical Society: 58, 563 - 568, (1962).

Procedures:

D.15.11.1 GoettscheF  The Goettsche's formula up to n-th degree
D.15.11.2 PPolyH  Poincare Polynomial of the Hilbert scheme of n points on a surface
D.15.11.3 BettiNumsH  Betti numbers of the Hilbert scheme of n points on a surface
D.15.11.4 MacdonaldF  The Macdonald's formula up to n-th degree
D.15.11.5 PPolyS  Poincare Polynomial of the n-th symmetric power of a variety
D.15.11.6 BettiNumsS  Betti numbers of the n-th symmetric power of a variety


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