3 results
Sharp Bertini Theorem for Plane Curves over Finite Fields
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 2 / June 2019
- Published online by Cambridge University Press:
- 07 January 2019, pp. 223-230
- Print publication:
- June 2019
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We prove that if
$C$ is a reflexive smooth plane curve of degree 
$d$ defined over a finite field 
$\mathbb{F}_{q}$ with 
$d\leqslant q+1$, then there is an 
$\mathbb{F}_{q}$-line 
$L$ that intersects 
$C$ transversely. We also prove the same result for non-reflexive curves of degree 
$p+1$ and 
$2p+1$ when 
$q=p^{r}$.
GENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTIC
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 2 / March 2020
- Published online by Cambridge University Press:
- 12 April 2018, pp. 647-661
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- March 2020
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In this paper, we study the singularities of a general hyperplane section
$H$ of a three-dimensional quasi-projective variety 
$X$ over an algebraically closed field of characteristic 
$p>0$. We prove that if 
$X$ has only canonical singularities, then 
$H$ has only rational double points. We also prove, under the assumption that 
$p>5$, that if 
$X$ has only klt singularities, then so does 
$H$.
SPECIALIZATION OF GRADED MODULES
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 2 / June 2002
- Published online by Cambridge University Press:
- 17 June 2002, pp. 491-506
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