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Global Brill–Noether theory over the Hurwitz space

Eric Larson, Hannah Larson and Isabel Vogt

Geometry & Topology 29 (2025) 193–257
Bibliography
1 E Ballico, C Keem, On linear series on general k-gonal projective curves, Proc. Amer. Math. Soc. 124 (1996) 7 MR1317030
2 S Billey, M Haiman, Schubert polynomials for the classical groups, J. Amer. Math. Soc. 8 (1995) 443 MR1290232
3 A Björner, F Brenti, Combinatorics of Coxeter groups, 231, Springer (2005) MR2133266
4 A Castorena, A López Martín, M Teixidor i Bigas, Petri map for vector bundles near good bundles, J. Pure Appl. Algebra 222 (2018) 1692 MR3763277
5 W Clifford, On the classification of loci, Philos. Trans. Roy. Soc. Lond. 169 (1878) 663
6 K Cook-Powell, D Jensen, Components of Brill–Noether loci for curves with fixed gonality, Michigan Math. J. 71 (2022) 19 MR4389812
7 K Cook-Powell, D Jensen, Tropical methods in Hurwitz–Brill–Noether theory, Adv. Math. 398 (2022) 108199 MR4372667
8 M Coppens, G Martens, Linear series on a general k-gonal curve, Abh. Math. Sem. Univ. Hamburg 69 (1999) 347 MR1722944
9 M Coppens, G Martens, Linear series on 4-gonal curves, Math. Nachr. 213 (2000) 35 MR1755245
10 M Coppens, G Martens, On the varieties of special divisors, Indag. Math. 13 (2002) 29 MR2014973
11 M Coppens, C Keem, G Martens, The primitive length of a general k-gonal curve, Indag. Math. 5 (1994) 145 MR1284560
12 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, III, Inst. Hautes Études Sci. Publ. Math. 28 (1966) 5 MR0217086
13 D Eisenbud, Commutative algebra: with a view toward algebraic geometry, 150, Springer (1995) MR1322960
14 D Eisenbud, J Harris, Limit linear series: basic theory, Invent. Math. 85 (1986) 337 MR0846932
15 D Eisenbud, J Harris, Irreducibility and monodromy of some families of linear series, Ann. Sci. École Norm. Sup. 20 (1987) 65 MR0892142
16 D Eisenbud, F O Schreyer, Relative Beilinson monad and direct image for families of coherent sheaves, Trans. Amer. Math. Soc. 360 (2008) 5367 MR2415078
17 K Eriksson, Reduced words in affine Coxeter groups, Discrete Math. 157 (1996) 127 MR1417291
18 C K Fan, Schubert varieties and short braidedness, Transform. Groups 3 (1998) 51 MR1603806
19 C K Fan, J R Stembridge, Nilpotent orbits and commutative elements, J. Algebra 196 (1997) 490 MR1475121
20 W Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math. 90 (1969) 542 MR0260752
21 W Fulton, R Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981) 271 MR0611386
22 D Gieseker, Stable curves and special divisors : Petri’s conjecture, Invent. Math. 66 (1982) 251 MR0656623
23 P Griffiths, J Harris, On the variety of special linear systems on a general algebraic curve, Duke Math. J. 47 (1980) 233 MR0563378
24 M D Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discrete Math. 99 (1992) 79 MR1158783
25 J Harris, D Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982) 23 MR0664324
26 M Hochster, Cohen–Macaulay varieties, geometric complexes, and combinatorics, from: "The mathematical legacy of Richard P Stanley" (editors P Hersh, T Lam, P Pylyavskyy, V Reiner), Amer. Math. Soc. (2016) 219 MR3618036
27 D Jensen, S Payne, Tropical independence, I : Shapes of divisors and a proof of the Gieseker–Petri theorem, Algebra Number Theory 8 (2014) 2043 MR3294386
28 D Jensen, D Ranganathan, Brill–Noether theory for curves of a fixed gonality, Forum Math. Pi 9 (2021) MR4199236
29 G Kempf, Schubert methods with an application to algebraic curves, technical report (1971)
30 S L Kleiman, D Laksov, On the existence of special divisors, Amer. J. Math. 94 (1972) 431 MR0323792
31 T Lam, L Lapointe, J Morse, A Schilling, M Shimozono, M Zabrocki, k-Schur functions and affine Schubert calculus, 33, Springer (2014) MR3379711
32 L Lapointe, J Morse, Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions, J. Combin. Theory Ser. A 112 (2005) 44 MR2167475
33 H K Larson, Refined Brill–Noether theory for all trigonal curves, Eur. J. Math. 7 (2021) 1524 MR4340946
34 H K Larson, A refined Brill–Noether theory over Hurwitz spaces, Invent. Math. 224 (2021) 767 MR4258055
35 H K Larson, Universal degeneracy classes for vector bundles on 1 bundles, Adv. Math. 380 (2021) 107563 MR4200467
36 A Lascoux, Ordering the affine symmetric group, from: "Algebraic combinatorics and applications" (editors A Betten, A Kohnert, R Laue, A Wassermann), Springer (2001) 219 MR1851953
37 R Lazarsfeld, Brill–Noether–Petri without degenerations, J. Differential Geom. 23 (1986) 299 MR0852158
38 Q Liu, Reduction and lifting of finite covers of curves, from: "Proceedings of the 2003 Workshop on Cryptography and Related Mathematics", Chuo Univ. (2003) 161
39 A Maroni, Le serie lineari speciali sulle curve trigonali, Ann. Mat. Pura Appl. 25 (1946) 343 MR0024182
40 G Martens, On curves of odd gonality, Arch. Math. (Basel) 67 (1996) 80 MR1392056
41 G Martens, F O Schreyer, Line bundles and syzygies of trigonal curves, Abh. Math. Sem. Univ. Hamburg 56 (1986) 169 MR0882414
42 B Osserman, A simple characteristic-free proof of the Brill–Noether theorem, Bull. Braz. Math. Soc. 45 (2014) 807 MR3296194
43 B Osserman, Connectedness of Brill–Noether loci via degenerations, Int. Math. Res. Not. 2019 (2019) 6162 MR4016895
44 S S Park, On the variety of special linear series on a general 5-gonal curve, Abh. Math. Sem. Univ. Hamburg 72 (2002) 283 MR1941560
45 N Pflueger, Brill–Noether varieties of k-gonal curves, Adv. Math. 312 (2017) 46 MR3635805
46 B Riemann, Grundlagen für eine allgemeine Theorie der Funkctionen einer veränderlichen complexen Größe, PhD thesis, Georg-August-Universität Göttingen (1851)
47 R P Stanley, On the number of reduced decompositions of elements of Coxeter groups, Eur. J. Combin. 5 (1984) 359 MR0782057
48 J R Stembridge, On the fully commutative elements of Coxeter groups, J. Algebraic Combin. 5 (1996) 353 MR1406459
49 J R Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997) 1285 MR1389789
50 J R Stembridge, The enumeration of fully commutative elements of Coxeter groups, J. Algebraic Combin. 7 (1998) 291 MR1616016