Algebraic intersection for translation surfaces in the stratum ℋ ( 2 )
| Autor: | Smaïl Cheboui, Arezki Kessi, Daniel Massart |
|---|---|
| Přispěvatelé: | Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Sequence General Mathematics media_common.quotation_subject 010102 general mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Infinity 01 natural sciences Infimum and supremum Combinatorics Intersection Genus (mathematics) Product (mathematics) 0103 physical sciences 010307 mathematical physics 0101 mathematics Algebraic number ComputingMilieux_MISCELLANEOUS media_common Mathematics |
| Zdroj: | Comptes Rendus. Mathématique Comptes Rendus. Mathématique, Académie des sciences (Paris), 2021, 359 (1), pp.65-70. ⟨10.5802/crmath.153⟩ |
| ISSN: | 1631-073X 1778-3569 |
| DOI: | 10.5802/crmath.153⟩ |
| Popis: | 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 $\mathcal{H}(2)$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|