Math @ Duke
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Publications [#347384] of Mark Haskins
Papers Published
- Mark, H; Hein, HJ; Johannes, N, Asymptotically cylindrical Calabi-Yau manifolds,
Journal of Differential Geometry, vol. 101 no. 2
(October, 2015),
pp. 213-265 [doi]
(last updated on 2024/04/23)
Abstract: Let M be a complete Ricci-flat Kähler manifold with one end and assume that this end converges at an exponential rate to [0, ∞) x X for some compact connected Ricci-flat manifold X. We begin by proving general structure theorems for M; in particular we show that there is no loss of generality in assuming that M is simply-connected and irreducible with Hol(M) = SU(n), where n is the complex dimension of M. If n > 2 we then show that there exists a projective orbifold M¯ and a divisor D¯ ∈ |-KM¯| with torsion normal bundle such that M is biholomorphic to M¯ \ D¯, thereby settling a long-standing question of Yau in the asymptotically cylindrical setting. We give examples where M¯ is not smooth: the existence of such examples appears not to have been noticed previously. Conversely, for any such pair (M¯, D¯) we give a short and self-contained proof of the existence and uniqueness of exponentially asymptotically cylindrical Calabi-Yau metrics on M¯ \ D¯.
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