# ag.algebraic geometry – Semi-stable sheaves on quadric surface

https://downloads.hindawi.com/journals/tswj/2014/346126.pdf

In this paper, Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials(E. Ballico and S.Huh), I have a question.

On the right down of the page 2 of this paper,

For every semistable 1-dimensional sheaf $$F$$ with $$chi_F(x, y)=mx+ny+t$$, define $$C_F:=mathrm {Supp}(F)$$ to be its scheme-theoretic support and then we have $$C_F in |O_Q(n, m)|$$.

Question : In this sentence, how we conclude that $$C_F in |O_Q(n, m)|$$?