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2 votes
1 answer
286 views

Markov triples and Newton-Okounkov bodies of $\mathbb{P}^2$

I am working on symplectic geometry and I have some questions about a degeneration of $\mathbb{P}^2$. Question: Can we obtain the moment polytope (or the polytope associated with the anti-canonical ...
Yunhyung Cho's user avatar
  • 1,047
15 votes
1 answer
828 views

symplectic form on an algebraic family

I know that smooth Fano varieties over $\mathbb{C}$ may be classified into a finite number of families in each dimension (1 in dimension 1, 10 in dimension 2, 105 in dimension 3 ...). I am ...
Nick L's user avatar
  • 6,995
4 votes
1 answer
458 views

Mirror symmetry for blowups of the projective plane

Let $S$ be a blowup of the projective plane $\mathbb{CP}^2$ at $n$ points. When $n\le 9$, Auroux, Katzarkov and Orlov showed that them a mirror Landau-Ginzburg model is given by a certain elliptic ...
Lee's user avatar
  • 41
4 votes
0 answers
152 views

Integrable systems with Fano phase space?

What are some known examples of finite-dimensional integrable systems with symplectic Fano phase space? Here by integrable system we mean a symplectic manifold $(X, \omega)$ of dimension $2n$ with $...
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