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arXiv · 2009.13876

Polystable log Calabi-Yau varieties and Gravitational instantons

Yuji Odaka
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Abstract

Open Calabi-Yau manifolds and log Calabi-Yau varieties have been broadly studied over decades. Regarding them as "semistable" objects, we propose to consider their good proper subclass, which we regard as certain poly-stable ones, morally corresponding to semistable with closed (minimal) orbits} as the classical analogue of GIT. We partially confirm that the new polystability seems equivalent to the existence of non-compact complete Ricci-flat Kahler metrics with small volume growths, notably many examples of gravitational instantons. Also, we prove some compactness or polystable reduction type results, partially motivated by bubbles of compact Ricci-flat metrics.

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Yuji Odaka. 2020-09-29. Polystable log Calabi-Yau varieties and Gravitational instantons. https://arxiv.org/abs/2009.13876

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