scholarly journals Homological congruence formulae for characteristic classes of singular varieties

2018 ◽  
Vol 5 (4) ◽  
pp. 1267-1292
Author(s):  
Laurentiu Maxim ◽  
Shoji Yokura
Keyword(s):  
Characteristic Classes ◽  
Singular Varieties

scholarly journals ALGEBRO-GEOMETRIC FEYNMAN RULES

2011 ◽  
Vol 08 (01) ◽  
pp. 203-237 ◽  
Author(s):  
PAOLO ALUFFI ◽  
MATILDE MARCOLLI
Keyword(s):  
General Procedure ◽  
Zeta Functions ◽  
Feynman Rule ◽  
Characteristic Classes ◽  
Partition Functions ◽  
Grothendieck Ring ◽  
Projective Varieties ◽  
Singular Varieties ◽  
Feynman Rules ◽  
Graph Hypersurface

We give a general procedure to construct "algebro-geometric Feynman rules", that is, characters of the Connes–Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In particular, this maps to the usual Grothendieck ring of varieties, defining "motivic Feynman rules". We also construct an algebro-geometric Feynman rule with values in a polynomial ring, which does not factor through the usual Grothendieck ring, and which is defined in terms of characteristic classes of singular varieties. This invariant recovers, as a special value, the Euler characteristic of the projective graph hypersurface complement. The main result underlying the construction of this invariant is a formula for the characteristic classes of the join of two projective varieties. We discuss the BPHZ renormalization procedure in this algebro-geometric context and some motivic zeta functions arising from the partition functions associated to motivic Feynman rules.

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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