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Mathematics > Algebraic Geometry

arXiv:1805.01323 (math)
This paper has been withdrawn by YongJoo Shin
[Submitted on 3 May 2018 (v1), last revised 4 May 2018 (this version, v2)]

Title:Global log canonical thresholds of minimal $(1,2)$-surfaces

Authors:In-Kyun Kim, YongJoo Shin, Joonyeong Won
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Abstract:Let $S$ be a minimal surface of general type with $p_g(S)=2$ and $K^2_S=1$, so called by a minimal $(1,2)$-surface. Then we obtain that the global log canonical threshold of the surface $S$ via $K_S$ is greater than equal to $\frac{1}{2}$. As an application we have \[ {\rm{vol}}(X)\ge\frac{4}{3}p_g(X)-\frac{10}{3} \] for all projective $3$-folds $X$ of general type which answers Question 1.4 of [J. A. Chen, M. Chen, C. Jiang, "The Noether inequality for algebraic threefolds", arXiv:1803.05553] about Noether inequality for $X$ with $5\le p_g(X)\le 26$.
Comments: Withdrawn by the authors due to an error in the proof of the main theorem
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14J17, 14J29, 14J30
Cite as: arXiv:1805.01323 [math.AG]
  (or arXiv:1805.01323v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.01323

Submission history

From: YongJoo Shin [view email]
[v1] Thu, 3 May 2018 14:29:35 UTC (7 KB)
[v2] Fri, 4 May 2018 14:00:21 UTC (1 KB) (withdrawn)
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