Geodesic
Constructing reducible Brill–Noether curves
Documenta mathematica, Tome 27 (2022), pp. 1953-1983 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

A fundamental problem in the theory of algebraic curves in projective space is to understand which reducible curves arise as limits of smooth curves of general moduli. Special cases of this question and variants have been critical in the resolution of many problems in the theory of algebraic curves over the past half century; examples include Sernesi's proof of the existence of components of the Hilbert scheme with the expected number of moduli when the Brill–Noether number is negative [E. Sernesi, Invent. Math. 75, 25–57 (1984; Zbl 0541.14024)], and Ballico's proof the Maximal Rank Conjecture for quadrics [E. Ballico, Lith. Math. J. 52, No. 2, 134–137 (2012; Zbl 1282.14054)]. In this paper, we give close-to-optimal bounds on this problem when the nodes are general points and the components are general in moduli. The results given here significantly extend those cases established by [Sernesi, loc. cit.], [Ballico, loc. cit.], and others. As explained in [Eric Larson, "Degenerations of curves in projective space and the maximal rank conjecture", Preprint (2018); arXiv:1809.05980], they also play a key role in the author's proof of the Maximal Rank Conjecture [Eric Larson, "The maximal rank conjecture", Preprint (2017); arXiv:1711.04906].
DOI : 10.4171/dm/x23
Classification : 14H10, 14H51
Mots-clés : degeneration, Brill-Noether theory, specialization 
@article{10_4171_dm_x23,
     author = {Eric Larson},
     title = {Constructing reducible {Brill{\textendash}Noether} curves},
     journal = {Documenta mathematica},
     pages = {1953--1983},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x23},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x23/}
}
TY  - JOUR
AU  - Eric Larson
TI  - Constructing reducible Brill–Noether curves
JO  - Documenta mathematica
PY  - 2022
SP  - 1953
EP  - 1983
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x23/
DO  - 10.4171/dm/x23
ID  - 10_4171_dm_x23
ER  - 
%0 Journal Article
%A Eric Larson
%T Constructing reducible Brill–Noether curves
%J Documenta mathematica
%D 2022
%P 1953-1983
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x23/
%R 10.4171/dm/x23
%F 10_4171_dm_x23
Eric Larson. Constructing reducible Brill–Noether curves. Documenta mathematica, Tome 27 (2022), pp. 1953-1983. doi: 10.4171/dm/x23

Cité par Sources :