  We quantitatively estimate the leading higher derivative corrections to
${\mathcal{N}}=1$ supergravity derived from IIB string compactifications and
study how they may affect moduli stabilisation and LVS inflation models. Using
the Kreuzer-Skarke database of 4D reflexive polytopes and their triangulated
Calabi-Yau database, we present scanning results for a set of divisor
topologies corresponding to threefolds with $1 \leq h^{1,1} \leq 5$. In
particular, we find several geometries suitable to realise blow-up inflation,
fibre inflation and poly-instantons inflation, together with a classification
of the divisors topologies for which the leading higher derivative corrections
to the inflationary potential vanish. In all other cases, we instead estimate
numerically how these corrections modify the inflationary dynamics, finding
that that they do not destroy the predictions for the main cosmological
observables.
