Annales Henri Lebesgue

Boulanger, Julien; Lanneau, Erwan; Massart, Daniel

Algebraic intersection for a family of Veech surfaces

Annales Henri Lebesgue, Volume 7 (2024), pp. 787-821.

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Keywords Lyapunov exponents, translation surface, Teichmüller curve, algebraic intersection

Abstract

We study some properties of the function $KVol$ defined by

KVol (X, ω) : = Vol (X, ω) sup_{α, β} \frac{Int (α, β)}{l_{g} (α) l_{g} (β)}

on the moduli space of translation surfaces. For the Teichmüller discs $𝒯_{n}$ of the original Veech surfaces arising from the right-angled triangles $(π / 2, π / n, (n - 2) π / 2 n)$ for odd $n \geq 5$ , we establish the first known explicit formula for $KVol$ (beyond the case of the moduli space of flat tori).

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