Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope
  Conjecture   We carry out a detailed intersection theoretic analysis of the
Deligne-Mumford compactification of the divisor on M_{10} consisting of curves
sitting on K3 surfaces. This divisor is not of classical Brill-Noether type,
and is known to give a counterexample to the Slope Conjecture. The computation
relies on the fact that this divisor has four different incarnations as a
geometric subvariety of the moduli space of curves, one of them as a higher
rank Brill-Noether divisor consisting of curves with an exceptional rank 2
vector bundle. As an application we describe the birational nature of the
moduli space of n-pointed curves of genus 10, for all n. We also show that on
M_{11} there are effective divisors of minimal slope and having large Iitaka
dimension. This seems to contradict the belief that on M_g the classical
Brill-Noether divisors are essentially the only ones of slope 6+12/(g+1).

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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat