Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On deformations of Q-factorial symplectic varieties   We shall prove that any small deformation of a Q-factorial projective
symplectic variety with terminal singularities is locally rigid; in other
words, it preserves the singularity. In particular, many singular symplectic
moduli of semi-stable sheaves on K3 have no smoothings via deformations. As an
application of the result, we also prove that the smootheness is preserved
under a flop in our symplectic case. We conjecture that a projective symplectic
variety has a smoothing by a flat deformation if and only if it has a crepant
(symplectic) resolution. This conjecture would be true if the minimal model
conjecture were true.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
20
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
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph