Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants of pure 2-dimensional sheaves inside threefolds and modular
  forms   Motivated by S-duality modularity conjectures in string theory, we study the
Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a
nonsingular threefold X in three different situations:
  (1). X is a K3 fibration over a curve. We study the Donaldson-Thomas
invariants of the 2 dimensional Gieseker stable sheaves in X supported on the
fibers. Analogous to the Gromov-Witten theory formula established in the work
of Maulik-Pandharipande, we express these invariants in terms of the Euler
characteristic of the Hilbert scheme of points on the K3 surface and the
Noether-Lefschetz numbers of the fibration, and prove that the invariants have
modular properties.
  (2). X is the total space of the canonical bundle of P^2. We study the
generalized Donaldson-Thomas invariants defined by Joyce-Song of the moduli
spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern
class equal to k times the class of the zero section of X. When k=1,2 or 3, and
semistability implies stability, we express the invariants in terms of known
modular forms. We prove a combinatorial formula for the invariants when k=2 in
the presence of the strictly semistable sheaves, and verify the BPS integrality
conjecture of Joyce-Song in some cases.
  (3). (Joint with Richard Thomas) X is a Calabi-Yau threefold and L is a
sufficiently positive line bundle. We define new invariants counting a
restricted class of 2-dimensional torsion sheaves, enumerating pairs (Z,H) in X
where H is a member of the linear system |L| and Z is a 1-dimensional subscheme
of H. The associated sheaf is the ideal sheaf of Z in H, pushed forward to X
and considered as a certain Joyce-Song pair in the derived category of X. We
express these invariants in terms of the MNOP invariants of X.

20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol