改进的Castelnuovo-Hüssen边界
Refining Castelnuovo-Halphen bounds
摘要：
使用$r\geq 4$、$d\gg s$、$r-1\leq s \leq 2r-4$和$π\geq 0$修复整数$r,d,s,π$。精化经典的结果的一个投影曲线的亏格，我们展示了一个尖锐的上界的算术亏格$p_a(C)$的积分投影曲线$C\subset {\mathbb{P}^r}$的程度$d$，假设$C$是不包含在任何表面的程度$<s$，不包含在任何表面的程度$s$与部分亏格$> π$。接下来，我们讨论其他类型的限制$p_a(C)$，涉及的条件，整个希尔伯特多项式的积分表面上的$C$可能谎言。
英文摘要：
Fix integers $r,d,s,π$ with $r\geq 4$, $d\gg s$, $r-1\leq s \leq 2r-4$, and $π\geq 0$. Refining classical results for the genus of a projective curve, we exhibit a sharp upper bound for the arithmetic genus $p_a(C)$ of an integral projective curve $C\subset {\mathbb{P}^r}$ of degree $d$, assuming that $C$ is not contained in any surface of degree $<s$, and not contained in any surface of degree $s$ with sectional genus $> π$. Next we discuss other types of bound for $p_a(C)$, involving conditions on the entire Hilbert polynomial of the integral surfaces on which $C$ may lie.
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