Singular

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)