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The setting is a square-tiled surface X. We study the quantity KVol, definedas the supremum over all pairs of closed curves, of their algebraicintersection divided by the product of their length, times the volume of X (soas to make it scaling-invariant). We give a hyperbolic-geometric constructionto compute KVol in a family of Teichm\H{u}ller disks of square-tiled surfaces.

Algebraic intersection for translation sufaces in a family of Teichm\H{u}ller disks