Brill-Noether loci

被引:0
作者
Teixidor i Bigas, Montserrat [1 ]
机构
[1] Tufts Univ, Math Dept, 177 Coll Ave, Medford, MA 02155 USA
关键词
LIMIT LINEAR SERIES; KODAIRA DIMENSION; MODULI SPACE; DIVISORS; BUNDLES; CURVES;
D O I
10.1007/s00229-025-01616-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Brill-Noether loci Mg,dr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {M}}<^>r_{g,d}$$\end{document} are those subsets of the moduli space Mg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {M}}_g$$\end{document} determined by the existence of a linear series of degree d and dimension r. By looking at non-singular curves in a neighborhood of a special chain of elliptic curves, we provide a new proof of the non-emptiness of the Brill-Noether loci when the expected codimension satisfies -g+r+1 <=rho(g,r,d)<= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-g+r+1\le \rho (g,r,d)\le 0$$\end{document} and prove that for a generic point of a component of this locus, the Petri map is onto. As an application, we show that Brill-Noether loci of the same codimension are distinct when the codimension is not too large, substantially generalizing the known result in codimensions 1 and 2. We also provide a new technique for checking that Brill-Noether loci are not included in each other.
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页数:17
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