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D. Eisenbud, A. Ven (1981)
On the normal bundles of smooth rational space curvesMathematische Annalen, 256
A. Alzati, R. Re, A. Tortora (2015)
An algorithm for the normal bundle of rational monomial curvesRendiconti del Circolo Matematico di Palermo Series 2, 67
J. Miret (1986)
On the variety of rational curves inPnAnnali dell’Università di Ferrara, 32
JM Miret (1986)
On the variety of rational curves in $${\mathbb{P}}^n$$ P nAnn. Univ. Ferrara Sez. VII Sc. Mat., 32
Izzet Coskun (2008)
Gromov-Witten invariants of jumping curvesTransactions of the American Mathematical Society, 360
A. Alzati, R. Re (2015)
Irreducible Components of Hilbert Schemes of Rational Curves with given Normal BundlearXiv: Algebraic Geometry
L Ramella (1993)
Sur les schémas définissant les courbes rationnelles lisses de $$\mathbb{P}^3$$ P 3 ayant fibré normal et fibré tangent restreint fixésMém. Soc. Math. France (N.S.), 54
Z. Ran (2003)
Normal Bundles of Rational Curves in Projective SpacesAsian Journal of Mathematics, 11
D. Eisenbud, A. Ven (1982)
On the variety of smooth rational space curves with given degree and normal bundleInventiones mathematicae, 67
F. Ghione, G. Sacchiero (1980)
Normal bundles of rational curves inP3manuscripta mathematica, 33
G Sacchiero (1980)
Fibrati normali di curvi razionali dello spazio proiettivoAnn. Univ. Ferrara Sez. VII, 26
L Ramella (1990)
La stratification du schéma de Hilbert des courbes rationnelles de $$\mathbb{P}^n$$ P n par le fibré tangent restreintC. R. Acad. Sci. Paris Sér. I Math., 311
Luciana Ramella (1993)
Sur les schémas définissant les courbes rationnelles lisses de $\mathbb {P}^3$ ayant fibré normal et fibré tangent restreint fixés, 54
G. Sacchiero (1982)
On the varieties parametrizing rational space curves with fixed normal bundlemanuscripta mathematica, 37
Gianni Sacchiero (1980)
Fibrati normali di curve razionali dello spazio proiettivoAnnali dell’Università di Ferrara, 26
A Alzati, R Re (2015)
$$PGL(2)$$ P G L ( 2 ) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundleJ. Pure Appl. Algebr., 219
A. Alzati, R. Re (2014)
PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundleJournal of Pure and Applied Algebra, 219
Let $$b_{\bullet }$$ b ∙ be a sequence of integers $$1 < b_1 \le b_2 \le \cdots \le b_{n-1}$$ 1 < b 1 ≤ b 2 ≤ ⋯ ≤ b n - 1 . Let $${\text {M}}_e(b_{\bullet })$$ M e ( b ∙ ) be the space parameterizing nondegenerate, immersed, rational curves of degree e in $$\mathbb {P}^n$$ P n such that the normal bundle has the splitting type $$\bigoplus _{i=1}^{n-1}\mathcal {O}(e+b_i)$$ ⨁ i = 1 n - 1 O ( e + b i ) . When $$n=3$$ n = 3 , celebrated results of Eisenbud, Van de Ven, Ghione and Sacchiero show that $${\text {M}}_e(b_{\bullet })$$ M e ( b ∙ ) is irreducible of the expected dimension. We show that when $$n \ge 5$$ n ≥ 5 , these loci are generally reducible with components of higher than the expected dimension. We give examples where the number of components grows linearly with n. These generalize an example of Alzati and Re.
Mathematische Zeitschrift – Springer Journals
Published: Aug 9, 2017
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