All Questions
7
questions
14
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520
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Am I missing something about this notion of Mirror Symmetry for abelian varieties?
This is a continuation of my recent question: Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s.
In the comments of the question, I was directed to the paper http://arxiv.org/abs/...
- 6,242
9
votes
2
answers
752
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Is the mirror of a hyperkaehler manifold always a hyperkaehler manifold?
Is the mirror of a hyperkaehler manifold always a hyperkaehler manifold?
What I know so far is as follows:
In this paper (https://arxiv.org/pdf/hep-th/9512195.pdf) by Verbitsky, it is claimed that ...
- 1,105
8
votes
0
answers
392
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Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s
It is well known (cf. Dolgachev) that there is a beautiful notion of mirror symmetry for lattice-polarized K3 surfaces. That is, if we are given a rank $r$ lattice $M$ of signature $(1, r - 1)$ and a ...
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3
votes
0
answers
188
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Toric degeneration of Kummer Surface
I am wondering if there are any explicit examples of a toric degeneration of a Kummer surface (e.g. as a family of projective varieties say), and what the central fibre can look like? (I am working ...
- 205
2
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0
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115
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Is there a hyperkaehler manifold whose mirror is the total space of a tangent/cotangent bundle?
I am looking for an example of a hyperkaehler manifold $Y$ whose mirror is the total space of a tangent bundle $TX$ or a cotangent bundle $T^*X$, where $X$ can be any Riemannian manifold.
Is such a ...
- 1,105
2
votes
0
answers
236
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Is the mirror of a noncompact hyperkaehler manifold also hyperkaehler?
This is essentially a follow-up question from 'Is the mirror of a hyperkaehler manifold always a hyperkaehler manifold?'. Verbitsky's theorem in (https://arxiv.org/pdf/hep-th/9512195.pdf) says that ...
- 1,105
2
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0
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321
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Stability notion to smoothing varieties under a flat deformation with a smooth total space
Is there any stability notion that led to an algebraic variety be smoothable in general for Fano varieties or for Calabi-Yau varieties?
Note that Friedman found a nesessary condition that $X$ to be ...
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