  We show an upper bound for the sum of positive Lyapunov exponents of any
Teichm\"uller curve in strata of quadratic differentials with at least one zero
of large multiplicity. As a corollary, it holds for any $SL(2,\mathbb
R)$-invariant subspaces defined over $\mathbb Q$ in these strata. This proves
Grivaux-Hubert's conjecture about the asymptotics of Lyapunov exponents for
strata with a large number of poles in the situation when at least one zero has
large multiplicity.
