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We prove results describing the structure of a Chow ring associated to a product of graphs, which arises from the Gross-Schoen desingularization of a product of regular proper semi-stable curves over discrete valuation rings. By the works of Johannes Kolb and Shou-Wu Zhang, this ring controls the behavior of the non-Archimedean height pairing on products of smooth proper curves over non-Archimedean fields. We provide a complete description of the degree map, and prove vanishing results affirming a conjecture of Kolb, which, combined with his work, leads to an analytic formula for the arithmetic intersection number of adelic metrized line bundles on products of curves over complete discretely valued fields.
A reciprocal linear space is the image of a linear space under coordinate-wise inversion. These fundamental varieties describe the analytic centers of hyperplane arrangements and appear as part of the defining equations of the central path of a linea
We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we to
In this paper, we prove a decomposition result for the Chow groups of projectivizations of coherent sheaves of homological dimension $le 1$. In this process, we establish the decomposition of Chow groups for the cases of Cayleys trick and standard fl
We consider proper, algebraic semismall maps f from a complex algebraic manifold X. We show that the topological Decomposition Theorem implies a motivic decomposition theorem for the rational algebraic cycles of X and, in the case X is compact, for t