Every morphism from to is constant if , and nonconstant morphisms from to rarely appear when . In this setting, Tango proved that a morphism from to is constant if . Here we focus on the case and show that if is the surjection onto a rank vector bundle inducing a morphism , then . Furthermore, a complete classification is given if equality holds.
Accepted:
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José Carlos Sierra 1
@article{CRMATH_2021__359_7_853_0, author = {Jos\'e Carlos Sierra}, title = {On morphisms from $\protect \mathbb{P}^3$ to $\protect \mathbb{G}(1,3)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {853--860}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {7}, year = {2021}, doi = {10.5802/crmath.219}, language = {en}, }
José Carlos Sierra. On morphisms from $\protect \mathbb{P}^3$ to $\protect \mathbb{G}(1,3)$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 853-860. doi : 10.5802/crmath.219. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.219/
[1] Rank two globally generated vector bundles with , Rend. Ist. Mat. Univ. Trieste, Volume 44 (2012), pp. 413-422 | MR | Zbl
[2] Une involution sur un espace de modules de fibrés instantons, Bull. Soc. Math. Fr., Volume 128 (2000) no. 4, pp. 577-584 | DOI | MR | Zbl
[3] -folds in of degree , Manuscr. Math., Volume 82 (1994) no. 3-4, pp. 393-406 | DOI | MR | Zbl
[4] 3264 and all that. A second course in algebraic geometry, Cambridge University Press, 2016 | DOI | Zbl
[5] Genre des courbes de l’espace projectif, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977) (Lecture Notes in Mathematics), Volume 687, Springer, 1978, pp. 31-59 | DOI | MR | Zbl
[6] Varieties of small codimension in projective space, Bull. Am. Math. Soc., Volume 80 (1974), pp. 1017-1032 | DOI | MR | Zbl
[7] Stable vector bundles of rank on , Math. Ann., Volume 238 (1978), pp. 229-280 | DOI | MR | Zbl
[8] Segre’s reflexivity and an inductive characterization of hyperquadrics, Memoirs of the American Mathematical Society, 763, American Mathematical Society, 2002 | DOI | Zbl
[9] On degrees and genera of curves on smooth quartic surfaces in , Nagoya Math. J., Volume 96 (1984), pp. 127-132 | DOI | MR | Zbl
[10] Sur les modules projectifs, Séminaire Dubreil. Algèbre et théorie des nombres, Volume 14 (1960-1961) no. 1, 2 | Numdam | Zbl
[11] Intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni, e a’ suoi punti tripli apparenti, Rend. Circ. Mat. Palermo, Volume 15 (1901), pp. 33-51 | DOI | Zbl
[12] On -dimensional projective spaces contained in the Grassmann variety , J. Math. Kyoto Univ., Volume 14 (1974), pp. 415-460 | DOI | MR | Zbl
[13] On morphisms from projective space to the Grassmann variety , J. Math. Kyoto Univ., Volume 16 (1976), pp. 201-207 | DOI | MR | Zbl
[14] On morphisms from projective space to the Grassmann variety . II, Bull. Kyoto Univ. Educ., Volume 64 (1984), pp. 1-20 | MR | Zbl
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