Algebraic intersection for translation surfaces in the stratum $\mathcal{H}(2)$

Abstract

We study the quantity $\mbox{KVol}$ defined as the supremum, over all pairs of closed curves, of their algebraic intersection, divided by the product of their lengths, times the area of the surface. The surfaces we consider live in the stratum $\mathcal{H}(2)$ of translation surfaces of genus $2$, with one conical point. We provide an explicit sequence $L(n,n)$ of surfaces such that $\mbox{KVol}(L(n,n)) \longrightarrow 2$ when $n$ goes to infinity, $2$ being the conjectured infimum for $\mbox{KVol}$ over $\mathcal{H}(2)$.

8 pages, 3 figures. arXiv admin note: text overlap with arXiv:2007.10847

Cited by in corpus (1)

• Intersection Number, Length, and Systole on Compact Hyperbolic Surfaces