Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques
  surface   We use wall-crossing in the Bridgeland stability manifold to systematically
study the birational geometry of the moduli space $M_\sigma(\mathbf{v})$ of
$\sigma$-semistable objects of class $\mathbf{v}$ for a generic stability
condition $\sigma$ on an arbitrary Enriques surface $X$. In particular, we show
that for any other generic stability condition $\tau$, the two moduli spaces
$M_\tau(\mathbf{v})$ and $M_\sigma(\mathbf{v})$ are birational. As a
consequence, we show that for primitive $\mathbf{v}$ of odd rank
$M_\sigma(\mathbf{v})$ is birational to a Hilbert scheme of points. Similarly,
in even rank we show that $M_\sigma(\mathbf{v})$ is birational to a moduli
space of torsion sheaves supported on a hyperelliptic curve when
$\ell(\mathbf{v})=1$. As an added bonus of our work, we prove that the
Donaldson-Mukai map
$\theta_{\mathbf{v},\sigma}:\mathbf{v}^\perp\to\mathrm{Pic}(M_\sigma(\mathbf{v}))$
is an isomorphism for these classes. Finally, we use our classification to
fully describe the geometry of the only two examples of moduli of stable
sheaves on $X$ that are uniruled (and thus not K-trivial).

5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org