Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A case study of intersections on blowups of the moduli of curves   We explain how logarithmic structures select natural principal components in
an intersection of schemes. These manifest in Chow homology and can be
understood using the geometry of strict transforms under logarithmic blowups.
Our motivation comes from Gromov--Witten theory. The toric contact cycles in
the moduli space of curves parameterize curves that admit a map to a fixed
toric variety with prescribed contact orders. We show that they are
intersections of virtual strict transforms of double ramification cycles in
blowups of the moduli space of curves. We supply a calculation scheme for the
virtual strict transforms, and deduce that toric contact cycles lie in the
tautological ring of the moduli space of curves. This is a higher dimensional
analogue of a result of Faber--Pandharipande. The operational Chow rings of
Artin fans play a basic role, and are shown to be isomorphic to rings of
piecewise polynomials on associated cone complexes. The ingredients in our
analysis are Fulton's blowup formula, Aluffi's formulas for Segre classes of
monomial schemes, piecewise polynomials, and degeneration methods. A model
calculation in toric intersection theory is treated without logarithmic methods
and may be read independently.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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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: comp-gas