
This article is cited in 4 scientific papers (total in 4 papers)
Chern classes of graph hypersurfaces and deletioncontraction relations
Paolo Aluffi^{} ^{} Mathematics Department, Florida State University, Tallahassee FL 32306, U.S.A.
Abstract:
We study the behavior of the Chern classes of graph hypersurfaces under the operation of deletioncontraction of an edge of the corresponding graph. We obtain an explicit formula when the edge satisfies two technical conditions, and prove that both these conditions hold when the edge is multiple in the graph. This leads to recursions for the Chern classes of graph hypersurfaces for graphs obtained by adding parallel edges to a given (regular) edge.
Analogous results for the case of Grothendieck classes of graph hypersurfaces were obtained in previous work, and both Grothendieck classes and Chern classes were used to define ‘algebrogeometric’ Feynman rules. The results in this paper provide further evidence that the polynomial Feynman rule defined in terms of the Chern–Schwartz–MacPherson class of a graph hypersurface reflects closely the combinatorics of the corresponding graph.
The key to the proof of the main result is a more general formula for the Chern–Schwartz–MacPherson class of a transversal intersection (see Section 3), which may be of independent interest. We also describe a more geometric approach, using the apparatus of ‘Verdier specialization’.
Key words and phrases:
Chern classes, graph hypersurfaces, deletioncontraction, Feynman rules.
DOI:
https://doi.org/10.17323/160945142012124671700
Full text:
http://www.mathjournals.org/.../2012012004001.html
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Bibliographic databases:
MSC: 14C17, 81Q30, 81T18, 05C75 Received: July 1, 2011; in revised form January 9, 2012
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Citation:
Paolo Aluffi, “Chern classes of graph hypersurfaces and deletioncontraction relations”, Mosc. Math. J., 12:4 (2012), 671–700
Citation in format AMSBIB
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\paper Chern classes of graph hypersurfaces and deletioncontraction relations
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\yr 2012
\vol 12
\issue 4
\pages 671700
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This publication is cited in the following articles:

Aluffi P., Faber E., “Splayed Divisors and their Chern Classes”, J. Lond. Math. Soc.Second Ser., 88:2 (2013), 563–579

P. Aluffi, “How many hypersurfaces does it take to cut out a Segre class?”, J. Algebra, 471 (2017), 480–491

Kulkarni A., Maxedon G., Yeats K., “Some Results on An AlgebroGeometric Condition on Graphs”, J. Aust. Math. Soc., 104:2 (2018), 218–254

Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59

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