We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point fornula to calculate the Hirzebruch Xy genus Xy(S[n]), where S[n] is the Hilbert scheme of points of length n of a surface 5. Combinatorial interpretation of t...We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point fornula to calculate the Hirzebruch Xy genus Xy(S[n]), where S[n] is the Hilbert scheme of points of length n of a surface 5. Combinatorial interpretation of the weights of the fixed points of the natural torus action on (C2)[n] is used. This is the first step to prove a conjectural formula about the elliptic genus of the Hilbert schemes.展开更多
文摘We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point fornula to calculate the Hirzebruch Xy genus Xy(S[n]), where S[n] is the Hilbert scheme of points of length n of a surface 5. Combinatorial interpretation of the weights of the fixed points of the natural torus action on (C2)[n] is used. This is the first step to prove a conjectural formula about the elliptic genus of the Hilbert schemes.
