Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal slope of tensor product of Hermitian vector bundles   We give an upper bound for the maximal slope of the tensor product of several
non-zero Hermitian vector bundles on the spectrum of an algebraic integer ring.
By Minkowski's theorem, we need to estimate the Arakelov degree of an arbitrary
Hermitian line subbundle $\bar M$ of the tensor product. In the case where the
generic fiber of $M$ is semistable in the sense of geometric invariant theory,
the estimation is established by constructing, through the classical invariant
theory, a special polynomial which does not vanish on the generic fibre of $M$.
Otherwise we use an explicte version of a result of Ramanan and Ramanathan to
reduce the general case to the former one.

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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: cs