Renato Vianna

activity

20162020

collaborators

3 papers

math.SG2020

Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type

Man-Wai Mandy Cheung, Renato Vianna

In this article we explore compactifications of cluster varieties of finite type in complex dimension two. Cluster varieties can be viewed as the spec of a ring generated by theta…

math.SG2019

Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ as $a + b + c \to \infty$

Weonmo Lee, Yong-Geun Oh, Renato Vianna

In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ associated to Markov triples $(a, b, c)$ describ…

math.SG2016

Infinitely many monotone Lagrangian tori in del Pezzo surfaces

Renato Vianna

We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for $C P^{2} #1 C P^{2}$ and $\mathb…

Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type

Asymptotic behavior of Vianna's exotic Lagrangian tori Ta,b,c​ in CP2 as a+b+c→∞

Infinitely many monotone Lagrangian tori in del Pezzo surfaces

Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a, b, c}$ in $CP^{2}$ as $a + b + c \to \infty$