Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Faltings' Delta-Invariant of Hyperelliptic Riemann Surfaces   In this paper we prove new explicit formulas for Faltings' $\delta$-invariant
of an arbitrary hyperelliptic Riemann surface. This has several applications:
For example we obtain an explicit lower bound for $\delta$ depending only on
the genus, and we deduce new explicit bounds for the Arakelov self-intersection
number $\omega^2$ associated to hyperelliptic curves over number fields.
Furthermore, we obtain an improved version of Szpiro's small points conjecture
for hyperelliptic curves of genus at least $3$. Our method allows us in
addition to establish a generalization of Rosenhain's formula on
$\theta$-derivatives conjectured by Gu\`ardia.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th