> | ### D.15.14 goettsche_lib Library: goettsche.lib Purpose: Drezet's formula for the Betti numbers of the moduli space of Kronecker modules, 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 References: [1] Drezet, Jean-Marc Cohomologie des varie'te's de modules de hauter nulle. Mathematische Annalen: 281, 43-85, (1988). [2] Goettsche, Lothar, The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface. Mathematische Annalen: 286, 193-208, (1990). [3] Macdonald, I. G., The Poincare polynomial of a symmetric product, Mathematical proceedings of the Cambridge Philosophical Society: 58, 563 - 568, (1962). Procedures:
> D.15.14.1 GoettscheF |  | The Goettsche's formula up to n-th degree
> D.15.14.2 PPolyH |  | Poincare Polynomial of the Hilbert scheme of n points on a surface
> D.15.14.3 BettiNumsH |  | Betti numbers of the Hilbert scheme of n points on a surface
> D.15.14.4 MacdonaldF |  | The Macdonald's formula up to n-th degree
> D.15.14.5 PPolyS |  | Poincare Polynomial of the n-th symmetric power of a variety
> D.15.14.6 BettiNumsS |  | Betti numbers of the n-th symmetric power of a variety
> D.15.14.7 PPolyN |  | Poincare Polynomial of the moduli space of Kronecker modules N (q; m, n)
> D.15.14.8 BettiNumsN |  | Betti numbers of the moduli space of Kronecker modules N (q; m, n)

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