Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some effective estimates for Andr\'e-Oort in $Y(1)^n$   Let $X\subset Y(1)^n$ be a subvariety defined over a number field $\mathbb F$
and let $(P_1,\ldots,P_n)\in X$ be a special point not contained in a
positive-dimensional special subvariety of $X$. We show that the if a
coordinate $P_i$ corresponds to an order not contained in a single exceptional
Siegel-Tatuzawa imaginary quadratic field $K_*$ then the associated
discriminant $|\Delta(P_i)|$ is bounded by an effective constant depending only
on $\operatorname{deg} X$ and $[{\mathbb F}:{\mathbb Q}]$. We derive analogous
effective results for the positive-dimensional maximal special subvarieties.
  From the main theorem we deduce various effective results of Andr\'e-Oort
type. In particular we define a genericity condition on the leading homogeneous
part of a polynomial, and give a fully effective Andr\'e-Oort statement for
hypersurfaces defined by polynomials satisfying this condition.

23
The categories of this paper are: solv-int
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat