2026-09-19T03:18:25Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/389592022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Isadore M. Singer.
Malmendier, Andreas
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2007-09-28T13:19:16Z
2007-09-28T13:19:16Z
2007
2007
http://hdl.handle.net/1721.1/38959
166327062
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 161-168).
The Donaldson invariants for CP2 were obtained as the u-plane integral from a N = 2 supersymmetric topological U(1)-gauge theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP2 as the stationary phase approximation of the low-energy effective U(I)-gauge theory on CP2 thus obtaining an interpretation of the u-plane integral in terms of determinant line bundles. For the product of the determinant line bundles, the local and global anomalies vanish. Moreover, the product has a canonical trivialization. We show that the u-plane integral also arises as the stationary phase approximation of a heterotic o-model on an elliptic curve at the boundary of the Coulomb branch with the target space CP1 x U(1). The semi-classical generating function is described in terms of determinant line bundles on the Coulomb branch. We show that in terms of the partition function on the elliptic curve, the blow-up function for the Donaldson invariants derived by Fintushel and Stern arises in a natural way.
by Andreas Malmendier.
Ph.D.
168 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Expressions for the generating function of the Donaldson invariants for CP²
Thesis
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