Lefschetz fibrations on adjoint orbits - PMA

More documents

Recommendations

Info

Main result Given H0 ∈ h and H ∈ hR with H a regular element. Then, the “height function ” fH : O (H0) → C defined by fH (x) = 〈H, x〉 x ∈ O (H0) has a finite number of isolated singularities and defines a <strong>Lefschetz</strong> fibration, that is, Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
<strong>Lefschetz</strong> <strong>fibrations</strong> from Lie theory the following properties hold: 1. The singularities are nondegenerate (Hessian non degenerate). 2. If c1, c2 ∈ C are regular values then the level manifolds f −1 H (c1) and f −1 H (c2) are diffeomorphic. 3. There exists a symplectic form Ω in O (H0) such that if c ∈ C is a regular value then the level manifold f −1 H (c) is symplectic, that is, the restriction of Ω to f −1 H (c) is a symplectic (nondegenerate) form. 4. If c ∈ C is a singular value, then f −1 H (c) contains affine subspaces (contained in O (H0)). These subspaces are symplectic with respect to the form Ω from the previous item. Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
Page 1 and 2: Lefschetz
Page 3 and 4: Motivation I want to explain the mo
Page 5 and 6: Motivation I want to explain the mo
Page 7 and 8: Mirror Symmetry for Calabi-Yaus To
Page 9 and 10: This is NOT the Hodge diamond Toric
Page 11 and 12: Basic Hodge Theory Theorem (Hodge D
Page 17 and 18: The Hodge Diamond h n,n h n,n−1 h
Page 19 and 20: Amusing consequence of the classica
Page 21 and 22: Example 1: Smooth Elliptic Curve h
Page 23 and 24: Example 3: Hodge Diamond of a CY th
Page 25 and 26: Hodge Diamonds of Mirror Pairs h n,
Page 27 and 28: Mirror Symmetry is a duality For ou
Page 29 and 30: Known cases of the HMS conjecture T
Page 31 and 32: AKO Mirror of a Del Pezzo Surface T
Page 33 and 34: Vanishing cycle - mathematician’s
Page 35 and 36: Fukaya category A category whose ob
Page 37 and 38: Fukaya-Seidel category Definition T
Page 39 and 40: Monodromy representation Since X \
Page 41 and 42: Symplectic Lefschetz</stron
Page 43 and 44: Symplectic structure on the blow-up
Page 45 and 46: A flag Elizabeth Gasparim L
Page 47: Adjoint orbit The adjoint represent
Page 51 and 52: What I think we proved Theorem The

Lefschetz fibrations on adjoint orbits - PMA

Create successful ePaper yourself

Delete template?

Save as template?