A reconstruction of Euler data

Authors:
Bong H. Lian, Chien-Hao Liu and Shing-Tung Yau

Journal:
J. Algebraic Geom. **12** (2003), 269-284

DOI:
https://doi.org/10.1090/S1056-3911-02-00311-9

Published electronically:
September 18, 2002

MathSciNet review:
1949644

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Abstract | References | Additional Information

Abstract: We apply the mirror principle (see *Mirror principle, I*, Asian J. Math. **1** (1997), pp. 729-763) to reconstruct the Euler data associated to a vector bundle on and a multiplicative class . This gives a direct way to compute the intersection number without referring to any other Euler data linked to . Here is the integral of the cohomology class of the induced bundle on a stable map moduli space. A package ```EulerData_MP.m`'' in Maple V that carries out the actual computation is provided in the electronic version `math.AG/0003071` of the current paper. For , the Chern polynomial, the computation of for the bundle , and , , for the bundles with are done using the code and are also included.

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Additional Information

**Bong H. Lian**

Affiliation:
National University of Singapore, Department of Mathematics, Singapore, 117543, Republic of Singapore

Email:
lian@brandeis.edu

**Chien-Hao Liu**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Email:
chienliu@math.harvard.edu

**Shing-Tung Yau**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Email:
yau@math.harvard.edu

DOI:
https://doi.org/10.1090/S1056-3911-02-00311-9

Received by editor(s):
October 9, 2000

Published electronically:
September 18, 2002

Additional Notes:
B. H. Lian is on leave from Brandeis University, Department of Mathematics, Waltham, Massachusetts 02154. This work is supported by DOE grant DE-FG02-88ER25065 and NSF grants DMS-9619884 and DMS-9803347