Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Vianna, Renato"'
Autor:
Cheung, Man-Wai Mandy, Vianna, Renato
Publikováno v:
2019-20 MATRIX Annals pp 567-602
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 functions and a compactification of such varieties can be given by a g
Externí odkaz:
http://arxiv.org/abs/2008.03265
Autor:
Casals, Roger, Vianna, Renato
This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieties. The construction uniformly recovers the full sequences for the Fib
Externí odkaz:
http://arxiv.org/abs/2004.13232
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori $T_{a,b,c}$ in $\mathbb{CP}^2$ associated to Markov triples $(a,b,c)$ described in \cite{Vi14}. We first prove that the Gromov capacity of the comp
Externí odkaz:
http://arxiv.org/abs/1904.11775
Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the invariant is
Externí odkaz:
http://arxiv.org/abs/1804.02044
Autor:
Vianna, Renato
We construct a family of Lagrangian tori $\Theta^n_s$ $\subset$ $(\mathbb{C}P^1)^n$, $s \in (0,1)$, where $\Theta^n_{1/2} = \Theta^n$, is the monotone twist Lagrangian torus described by Chekanov-Schlenk. We show that for $n = 2m$ and $s \ge 1/2$ the
Externí odkaz:
http://arxiv.org/abs/1603.02006
Autor:
Vianna, Renato
We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for $\mathbb{C}P^2 \# 1 \overline{\mathbb{C}P^2}$ and $\mathbb{C}P^2 \# 2 \overline{\mathbb{C}P^2}$ , we are able to get almost tor
Externí odkaz:
http://arxiv.org/abs/1602.03356
Autor:
Tonkonog, Dmitry, Vianna, Renato
Publikováno v:
J. Symp. Geom. 16:5 (2018) 1409-1454
We introduce a new version of Floer theory of a non-monotone Lagrangian submanifold which only uses least area holomorphic disks with boundary on it. We use this theory to prove non-displaceability theorems about continuous families of Lagrangian tor
Externí odkaz:
http://arxiv.org/abs/1511.00891
Autor:
Vianna, Renato
Publikováno v:
Journal of Topology 2016
Related to each degeneration from CP^2 to CP(a^2,b^2,c^2), for (a,b,c) a Markov triple - positive integers satisfying a^2 + b^2 + c^2 = 3abc - there is a monotone Lagrangian torus, which we call T(a^2,b^2,c^2). We employ techniques from symplectic fi
Externí odkaz:
http://arxiv.org/abs/1409.2850
Autor:
Vianna, Renato
Publikováno v:
Geom. Topol. 18 (2014) 2419-2476
We construct an exotic monotone Lagrangian torus in CP^2 using techniques motivated by mirror symmetry. We show that it bounds 10 families of Maslov index 2 holomorphic discs, and it follows that this exotic torus is not Hamiltonian isotopic to the k
Externí odkaz:
http://arxiv.org/abs/1305.7512