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Let E : 0 ! S ! E ! Q ! 0 be a short exact sequence of hermitian vector bundles with metrics on S and Q induced from that on E. We compute the Bott-Chern form áe(E ) corresponding to any characteri...
Let F be the complete °ag variety over SpecZ with the tautological ˉltration 0 ½ E1 ½ E2 ½ ¢ ¢ ¢ ½ En = E of the trivial bundle E of rank n over F. The trivial hermitian metric o...
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
Deligne and Rapoport developed the theory of generalized elliptic curves over arbitrary schemes and they proved that various moduli stacks for (ample) “level-N” structures on generalized elliptic cu...
In this short note, we give another proof of the Geometric-Arithmetic Mean inequality.
Mixed arithmetic and geometric means, with and without weights, are both considered. Related to mixed arithmetic and geometric means, the following three types of inequalities and their generalization...

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