Lefschetz fibrations on adjoint orbits - PMA

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Basic Hodge Theory Theorem (Hodge Decomposition Theorem) Let X be a compact Kähler manifold of dimension n. Then there exists a decomposition H k (X , C) = H p,q (X ) p+q=k Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
Basic Hodge Theory Theorem (Hodge Decomposition Theorem) Let X be a compact Kähler manifold of dimension n. Then there exists a decomposition H k (X , C) = H p,q (X ) Classical Symmetries: p+q=k 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: This is NOT the Hodge diamond Toric
Page 13 and 14: Basic Hodge Theory Theorem (Hodge D
Page 15 and 16: 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 and 48: Adjoint orbit The adjoint represent
Page 49 and 50: Lefschetz
Page 51 and 52: What I think we proved Theorem The

Lefschetz fibrations on adjoint orbits - PMA

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