Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fourth adjoint Contractions of divisorial and fiber types   In this paper, we will list up all the cases for the ray contractions of
divisorial and fiber types for smooth projective varieties of dimension five.
These are obtained as a corollary from the lists of n-dimensional k-th adjoint
contractions f: X -> Y of the same types for k=1,2,3 and 4 (n> or =5). The
lists for k=1,2 and 3 have previously been obtained in [Na], Proposition 1.2
and Theorem 1.3. The main task will be to have such a list for k=4, where one
case in the list fails to show that a positive-dimensional general fiber F of f
is irreducible when n>5. This assertion will, however, be proven when n=5 with
an essential aid of 3-dimensional Minimal Model Program in [Mo2]. (We do not
show the existence of cases.)

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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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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: nucl-th
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The categories of this paper are: nlin
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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: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ex