Lefschetz fibrations on adjoint orbits - PMA

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Compact Calabi Yaus are few... ◮ 1D: Only tori, hence elliptic curves in the algebraic case. ◮ 2D: K3 surfaces, possibly a couple more examples depending on your definition. ◮ 3D: Quintic on P 4 , and unknown classification, open problem, conjecturally there are finitely many. Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
Mirror Symmetry is a duality For our CYs: The duality is: Calabi–Yau = trivial canonical bundle trivial cotangent bundle ⇔ parallelizable manifold vector space ⇔ dual vector space tangent bundle ⇔ cotangent bundle complex geometry ⇔ symplectic geometry 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: Hodge Diamonds of Mirror Pairs h n,
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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