A Characterization of Complete Intersection Curves in P 3

1988 ◽  
Vol 104 (3) ◽  
pp. 711 ◽  
Author(s):  
Rosario Strano
Keyword(s):  
Complete Intersection ◽  
Intersection Curves

scholarly journals A SPLITTING CRITERION FOR RANK 2 BUNDLES ON A GENERAL SEXTIC THREEFOLD

2004 ◽  
Vol 15 (04) ◽  
pp. 341-359 ◽  
Author(s):  
LUCA CHIANTINI ◽  
CARLO MADONNA
Keyword(s):  
Vector Bundle ◽  
Complete Intersection ◽  
Splitting Criterion ◽  
Rank 2 ◽  
Intersection Curves ◽  
Rank 2 Bundles

In this paper we show that on a general sextic hypersurface X⊂ℙ4, a rank 2 vector bundle ℰ splits if and only if h1(ℰ(n))=0 for any n∈ℤ. We get thus a characterization of complete intersection curves in X.

scholarly journals K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

2021 ◽  
pp. 1-41
Author(s):  
KENNETH ASCHER ◽  
KRISTIN DEVLEMING ◽  
YUCHEN LIU
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Moduli Of Curves ◽  
Quadric Surface ◽  
Intersection Curves

Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.

Polynomial parametrization of nonsingular complete intersection curves

2007 ◽  
Vol 18 (5) ◽  
pp. 483-493
Author(s):  
Toufiq Benbouziane ◽  
Hassan El Houari ◽  
M’hammed El Kahoui
Keyword(s):  
Complete Intersection ◽  
Intersection Curves

A note on special cubic fourfolds of small discriminants

2021 ◽  
Vol 33 (5) ◽  
pp. 1137-1155
Author(s):  
Hoang Le Truong ◽  
Hoang Ngoc Yen
Keyword(s):  
Complete Intersection ◽  
Rational Surface ◽  
Explicit Construction ◽  
Smooth Surfaces ◽  
Liaison Class ◽  
Cubic Fourfold

Abstract In this paper, our purpose is to give a characterization of the generic special cubic fourfold which contains a smooth rational surface of degree 9 not homologous to a complete intersection. As corollaries, we will give an explicit construction of families of smooth surfaces in generic special cubic fourfolds X ∈ 𝒞 δ {X\in\mathcal{C}_{\delta}} for 6 < δ ≤ 30 {6<\delta\leq 30} and δ ≡ 0 ( mod 6 ) {\delta\equiv 0~{}(\bmod~{}6)} . This applies in particular to give an explicit construction of two different liaison class of smooth surfaces in all such special cubic fourfolds with the prescribed invariants.

scholarly journals The gonality of complete intersection curves

2020 ◽  
Vol 560 ◽  
pp. 579-608 ◽  
Author(s):  
James Hotchkiss ◽  
Chung Ching Lau ◽  
Brooke Ullery
Keyword(s):  
Complete Intersection ◽  
Intersection Curves
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