Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit biregular/birational geometry of affine threefolds: completions
  of A^3 into del Pezzo fibrations and Mori conic bundles   We study certain pencils of del Pezzo surfaces generated by a smooth del
Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a
weighted projective space P and an appropriate multiple of a hyperplane H. Our
main observation is that every minimal model program relative to the morphism
lifting such pencil on a suitable resolution of its indeterminacies preserves
the open subset P H \^a A^3. As an application, we obtain projective
completions of A^3 into del Pezzo fibrations over P^1 of every degree less or
equal to 4. We also obtain completions of A^3 into Mori conic bundles, whose
restrictions to A^3 are twisted C*-fibrations over A^2 .

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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph