By R. Keith Dennis

ISBN-10: 3540119663

ISBN-13: 9783540119661

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10. 11. 12. and R. Pandharipande. Notes on stable W. Fulton maps and quantum cohoAmer. Math. Cruz 1995, pages 45-96. geometry-Santa mology. , Providence, RI, 1997. Math. Res. invariants. Internat. Gromov-Witten A. Givental. Equivariant 1996(13):613-663. Notices, Localization of virtual classes. Invent. T. Graber and R. Pandhaxipande. , 1999. 135:487-518, 13. M. Kontsevich. space of curves of rational Enumeration (Texel Island, 1994), curves via torus pages 335-368. In The moduli actions. Birkhiiuser Boston, Boston, MA, 1995.

In order to define can simply apply Noether's theorem for a gauge 0-term we are multiplying charge, constant, U(1) topological we in the unbroken transformation in the 0 U(1) direction of corresponding Noether given, after N= ag the 0-term f d 3 x0i (0 An infinitesimal gauge by D,,O, (1-59) 0. charge, N= be [18]. be defined ag 60 to the direction would I will F attvFav. - becomes action transformation The (1-55) , Dyon Effect. 61) C6sar G6mez and Rafael 50 or, in charge, electric of the terms HernAndez as Og e N -- + - Notice (1-61) from ground of the rotation, we that If e which electric that implies charge lagrangian, if we 27ri( '+jt2 'Tm) 9 ng N = f.

3): as Y where = a (,r, d, 7) graphs FM-g,n (IF, d)T] given by (-r, d, -y). Then have 0 (9 ... 3) an) t7MWg,n(PI,d)] T 0 VI FMg,n (Pl,d)T] b* ev* (a, an) K. Behrend 28 The fixed Recall locus that prestable graphs are They modular marked F, (which either can be tails graphs that the of consist curves. pair or edges), up to markings of the vertices, giving the vertices and edges E,. The set of flags connected with A vertex (the is (-r, d,,y) be least at of -r' a 1 non-negative Tails the vertex v graph is a valence valence by contracting is obtained The set of vertices vertices.

### Algebraic K-theory. Proc. Oberwolfach 1980 by R. Keith Dennis

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