scholarly journals Universal secant bundles and syzygies of canonical curves

2020 ◽  
Author(s):  
Michael Kemeny
Keyword(s):  
Canonical Curves

scholarly journals Canonical curves of genus eight

2003 ◽  
Vol 79 (3) ◽  
pp. 59-64
Author(s):  
Manabu Ide ◽  
Shigeru Mukai
Keyword(s):  
Canonical Curves

CANONICAL CURVES IN ℙ3

2002 ◽  
Vol 85 (2) ◽  
pp. 333-366 ◽  
Author(s):  
JACQUELINE ROJAS ◽  
ISRAEL VAINSENCHER
Keyword(s):  
Vector Space ◽  
Hilbert Scheme ◽  
Linear Component ◽  
Arithmetic Genus ◽  
Generic Point ◽  
Rational Map ◽  
Linear Forms ◽  
Cubic Surface ◽  
Canonical Curve ◽  
Canonical Curves

Let ${\rm Hilb}^{6t-3}(\mathbb{P}^3)$ be the Hilbert scheme of closed 1-dimensional subschemes of degree 6 and arithmetic genus 4 in $\mathbb{P}^3$. Let $H$ be the component of ${\rm Hilb}^{6t-3}(\mathbb{P}^3)$ whose generic point corresponds to a canonical curve, that is, a complete intersection of a quadric and a cubic surface in $\mathbb{P}^3$. Let $F$ be the vector space of linear forms in the variables $z_1, z_2, z_3, z_4$. Denote by $F_d$ the vector space of homogeneous forms of degree $d$. Set $X = \{(f_2,f_3)\}$ where $f_2 \in \mathbb{P}(F_2)$ is a quadric surface, and $f_3 \in \mathbb{P}(F_3/f_2 \cdot F)$ is a cubic modulo $f_2$. We have a rational map, $\sigma : X \cdots \rightarrow H$ defined by $(f_2,f_3) \mapsto f_2 \cap f_3$. It fails to be regular along the locus where $f_2$ and $f_3$ acquire a common linear component. Our main result gives an explicit resolution of the indeterminacies of $\sigma$ as well as of the singularities of $H$. 2000 Mathematical Subject Classification: 14C05, 14N05, 14N10, 14N15.

Sign in / Sign up

Export Citation Format

Share Document