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- W1870069377 abstract "Let $M$ be a complete Ricci-flat Kähler manifold with one end and assume that this end converges at an exponential rate to $[0,infty) times X$ 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 $mathrm{Hol}(M) = mathrm{SU}(n)$, where $n$ is the complex dimension of $M$. If $n gt 2$ we then show that there exists a projective orbifold $overline{M}$ and a divisor $overline{D} in lvert -K_{overline{M}} rvert$ with torsion normal bundle such that $overline{M}$ is biholomorphic to $overline{M} setminus overline{D}$, thereby settling a long-standing question of Yau in the asymptotically cylindrical setting.We give examples where $overline{M}$ is not smooth: the existence of such examples appears not to have been noticed previously. Conversely, for any such pair $overline{M} setminus overline{D}$ we give a short and self-contained proof of the existence and uniqueness of exponentially asymptotically cylindrical Calabi–Yau metrics on $overline{M} setminus overline{D}$." @default.
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- W1870069377 date "2015-10-01" @default.
- W1870069377 modified "2023-09-30" @default.
- W1870069377 title "Asymptotically cylindrical Calabi–Yau manifolds" @default.
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- W1870069377 doi "https://doi.org/10.4310/jdg/1442364651" @default.
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