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A direct paternal-line descendent of Dante, which Sperello Alighieri might very well be, would essentially share a copy of Dante's Y-DNA, which is about 2% of the human genome. This is comparable to something between 2nd cousin (3.13%) and 3rd cousin (1.5%).

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Dante has no living paternal-line descendants. The reason for the unusual (for Italy) double last name Serego Alighieri was to preserve the Alighieri name despite there being only female descendants left at the time (in the 1500s). Source: https://it.m.wikipedia.org/wiki/Alighieri#Storia_familiare (in Italian)

Would you care to elaborate? You're talking about the Y of the XY chromosomes?

If Dante’s son had a son who had a son x 36, the Y chromosome would not have changed much

Assuming all those 36 sons were actually children of their legal fathers.

In general you can say that on average a child has 25% of their genes from each grandparent. But in the case of the sex chromosomes, we know that a male has 50% of their paternal grandfather's sex chromosomes and 0% of their paternal grandmother's sex chromosomes (and vice versa for a female); the Y chromosome is passed on whole or not at all (you can't get half of it from your mother).

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