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A special Calabi-Yau degeneration with trivial monodromy
Algebraic Geometry · Submitted 4 Dec 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds.
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The abstract, sentence by sentence
A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. | background 1.00 | 0.02 | 0.04 | asserted 1.00 |
| s1 | We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds. | result 0.57 | 0.94 | 0.91 | asserted 1.00 |
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The paper
Original abstract
A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds.
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What this paper does with the arXiv papers it cites
What it cites · 2 sentences without a confident label
Uses the method or tool of 1 paper
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A simple way to determine the monodromy on $H^3(Y_t)$ is using the Picard-Fuchs operator $𝒫$ of the family that was determined in [ref] .
Picard-Fuchs operators for octic arrangements I (The case of orphans) · Construction of $Δ$ · 0.91
Cites as background 1 paper
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For more information on special double octics we refer to [ref] , [ref] .
Classification of double octic Calabi-Yau threefolds · Double octics · 0.98
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