Geodesic
A Vanishing Theorem for the Twisted Normal Bundle of Curves in $\mathbb{P}^{n}$, $n\geqslant 8$
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 1-5

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the existence of a smooth and non-degenerate curve $X\subset \mathbb{P}^{n}$, $n\geqslant 8$, with $\deg (X)=d$, $p_{a}(X)=g$, $h^{1}(N_{X}(-1))=0$, and general moduli for all $(d,g,n)$ such that $d\geqslant (n-3)\lceil g/2\rceil +n+3$. It was proved by C. Walter that, for $n\geqslant 4$, the inequality $2d\geqslant (n-3)g+4$ is a necessary condition for the existence of a curve with $h^{1}(N_{X}(-1))=0$.
DOI : 10.4153/S0008439519000146
Mots-clés : projective curve, normal bundle, twisted normal bundle 
Ballico, E. A Vanishing Theorem for the Twisted Normal Bundle of Curves in $\mathbb{P}^{n}$, $n\geqslant 8$. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 1-5. doi: 10.4153/S0008439519000146
@article{10_4153_S0008439519000146,
     author = {Ballico, E.},
     title = {A {Vanishing} {Theorem} for the {Twisted} {Normal} {Bundle} of {Curves} in $\mathbb{P}^{n}$, $n\geqslant 8$},
     journal = {Canadian mathematical bulletin},
     pages = {1--5},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S0008439519000146},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000146/}
}
TY  - JOUR
AU  - Ballico, E.
TI  - A Vanishing Theorem for the Twisted Normal Bundle of Curves in $\mathbb{P}^{n}$, $n\geqslant 8$
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 1
EP  - 5
VL  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000146/
DO  - 10.4153/S0008439519000146
ID  - 10_4153_S0008439519000146
ER  - 
%0 Journal Article
%A Ballico, E.
%T A Vanishing Theorem for the Twisted Normal Bundle of Curves in $\mathbb{P}^{n}$, $n\geqslant 8$
%J Canadian mathematical bulletin
%D 2020
%P 1-5
%V 63
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000146/
%R 10.4153/S0008439519000146
%F 10_4153_S0008439519000146

[1] Atanasov, A., Interpolation and vector bundles on curves. Google Scholar

[2] Atanasov, A., Larson, E., and Yang, D., Interpolation for normal bundles of general curves. Google Scholar

[3] Ballico, E. and Ellia, P., Bonnes petites composantes des schémas de Hilbert de courbes lisses de ℙn. C. R. Acad. Sci. Paris Sér. I Math. 306(1988), no. 4, 187–190. Google Scholar

[4] Ellingsrud, G. and Hirschowitz, A., Sur le fibré normal des courbes gauches. C. R. Acad. Sci. Paris Sér. I Math. 299(1984), no. 7, 245–248. Google Scholar

[5] Hartshorne, R. and Hirschowitz, A., Smoothing algebraic space curves. In: Algebraic geometry. Lecture Notes in Math., 1124, Springer, Berlin, 1985, pp. 98–131. https://doi.org/10.1007/BFb0074998 Google Scholar

[6] Larson, E., Interpolation for restricted tangent bundles of general curves. Algebra Number Theory 10(2016), no. 4, 931–938. https://doi.org/10.2140/ant.2016.10.931 Google Scholar

[7] Larson, E., Constructing reducible Brill–Noether curves. Google Scholar

[8] Larson, E., The generality of a section of a curve. Google Scholar

[9] Larson, E., Interpolation with bounded error. Google Scholar

[10] Larson, E. and Vogt, I., Interpolation for Brill–Noether curve in ℙ4. Google Scholar

[11] Perrin, D., Courbes passant par m points généraux de 3. Mém. Math. France, Mem. no. 28/29, 1987. Google Scholar

[12] Ran, Z., Normal bundles of rational curves in projective spaces. Asian J. Math. 11(2007), no. 4, 567–608. https://doi.org/10.4310/AJM.2007.v11.n4.a3 Google Scholar

[13] Sacchiero, G., Normal bundle of rational curves in projective space. Ann. Univ. Ferrara Sez. VII (N.S.) 26(1981), 33–40. Google Scholar

[14] Sernesi, E., On the existence of certain families of curves. Invent. Math. 75(1984), 25–57. https://doi.org/10.1007/BF01403088 Google Scholar

[15] Vogt, I., Interpolation for Brill-Noether space curves. Manuscripta Math. 156(2018), 137–147. https://doi.org/10.1007/s00229-017-0961-4 Google Scholar

[16] Walter, C., Hyperplane sections of arithmetically Cohen–Macaulay curves. Proc. Amer. Math. Soc. 123(1995), no. 9, 2651–2656. Google Scholar

Cité par Sources :