Consider the family of singular hyperelliptic curves $$ y^2 - x(x-1)^2(x-2)(x-3)(x-4)(x-t) $$ over $\mathbb{A}^1_t$. Over a generic point the fiber is a genus three curve where one of the genera comes from a nodal degeneration. Over any of the singular points except for $1$ there is a degeneration to a genus 3 curve with two nodal degenerations. Around these points I can use the picard-lefschetz formula to describe the monodromy, but I am at a loss as to how to describe the monodromy around $t=1$. Are there any tools for accomplishing this?
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