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- W4300851258 abstract "Let $M$ be a complete Ricci-flat Kahler 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 Hol$(M)$ $=$ SU$(n)$, where $n$ is the complex dimension of $M$. If $n > 2$ we then show that there exists a projective orbifold $bar{M}$ and a divisor $bar{D}$ in $|{-K_{bar{M}}}|$ with torsion normal bundle such that $M$ is biholomorphic to $bar{M}setminusbar{D}$, thereby settling a long-standing question of Yau in the asymptotically cylindrical setting. We give examples where $bar{M}$ is not smooth: the existence of such examples appears not to have been noticed previously. Conversely, for any such pair $(bar{M}, bar{D})$ we give a short and self-contained proof of the existence and uniqueness of exponentially asymptotically cylindrical Calabi-Yau metrics on $bar{M}setminusbar{D}$." @default.
- W4300851258 created "2022-10-04" @default.
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- W4300851258 date "2012-12-31" @default.
- W4300851258 modified "2023-10-06" @default.
- W4300851258 title "Asymptotically cylindrical Calabi-Yau manifolds" @default.
- W4300851258 doi "https://doi.org/10.48550/arxiv.1212.6929" @default.
- W4300851258 hasPublicationYear "2012" @default.
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