Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
The nonabelian Brill–Noether divisor on $\overline{\mathcal{M}}_{13}$ and the Kodaira dimension of $\overline{\mathcal{R}}_{13}$

Gavril Farkas, David Jensen and Sam Payne

Geometry & Topology 28 (2024) 803–866
Bibliography
1 D Agostini, I Barros, Pencils on surfaces with normal crossings and the Kodaira dimension of g,n, Forum Math. Sigma 9 (2021) MR4247637
2 Y An, M Baker, G Kuperberg, F Shokrieh, Canonical representatives for divisor classes on tropical curves and the matrix-tree theorem, Forum Math. Sigma 2 (2014) MR3264262
3 M Aprodu, G Farkas, Koszul cohomology and applications to moduli, from: "Grassmannians, moduli spaces and vector bundles" (editors D A Ellwood, E Previato), Clay Math. Proc. 14, Amer. Math. Soc. (2011) 25 MR2807847
4 M Aprodu, G Farkas, Ş Papadima, C Raicu, J Weyman, Topological invariants of groups and Koszul modules, Duke Math. J. 171 (2022) 2013 MR4484204
5 E Arbarello, M Cornalba, P A Griffiths, J Harris, Geometry of algebraic curves, I, 267, Springer (1985) MR770932
6 A Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977) 149 MR0572974
7 A Bertram, B Feinberg, On stable rank two bundles with canonical determinant and many sections, from: "Algebraic geometry" (editor P E Newstead), Lecture Notes in Pure and Appl. Math. 200, Dekker (1998) 259 MR1651099
8 R Biggers, M Fried, Irreducibility of moduli spaces of cyclic unramified covers of genus g curves, Trans. Amer. Math. Soc. 295 (1986) 59 MR0831188
9 G Bruns, 15 is of general type, Algebra Number Theory 10 (2016) 1949 MR3576116
10 D Chen, G Farkas, I Morrison, Effective divisors on moduli spaces of curves and abelian varieties, from: "A celebration of algebraic geometry" (editors B Hassett, J McKernan, J Starr, R Vakil), Clay Math. Proc. 18, Amer. Math. Soc. (2013) 131 MR3114939
11 A Chiodo, D Eisenbud, G Farkas, F O Schreyer, Syzygies of torsion bundles and the geometry of the level modular variety over g, Invent. Math. 194 (2013) 73 MR3103256
12 F Cools, J Draisma, S Payne, E Robeva, A tropical proof of the Brill–Noether theorem, Adv. Math. 230 (2012) 759 MR2914965
13 M Coppens, G Martens, Linear series on a general k–gonal curve, Abh. Math. Sem. Univ. Hamburg 69 (1999) 347 MR1722944
14 E Cotterill, A Alonso Gonzalo, N Zhang, The strong maximal rank conjecture and higher rank Brill–Noether theory, J. Lond. Math. Soc. 104 (2021) 169 MR4313243
15 D Eisenbud, J Harris, Limit linear series: basic theory, Invent. Math. 85 (1986) 337 MR0846932
16 D Eisenbud, J Harris, The Kodaira dimension of the moduli space of curves of genus 23, Invent. Math. 90 (1987) 359 MR0910206
17 G Farkas, Koszul divisors on moduli spaces of curves, Amer. J. Math. 131 (2009) 819 MR2530855
18 G Farkas, Brill–Noether with ramification at unassigned points, J. Pure Appl. Algebra 217 (2013) 1838 MR3053519
19 G Farkas, D Jensen, S Payne, The Kodaira dimensions of 22 and 23, preprint (2020) arXiv:2005.00622v2
20 G Farkas, K Ludwig, The Kodaira dimension of the moduli space of Prym varieties, J. Eur. Math. Soc. 12 (2010) 755 MR2639318
21 G Farkas, M Popa, Effective divisors on g, curves on K3 surfaces, and the slope conjecture, J. Algebraic Geom. 14 (2005) 241 MR2123229
22 G Farkas, R Rimányi, Quadric rank loci on moduli of curves and K3 surfaces, Ann. Sci. Éc. Norm. Supér. 53 (2020) 945 MR4157107
23 G Farkas, A Verra, Prym varieties and moduli of polarized Nikulin surfaces, Adv. Math. 290 (2016) 314 MR3451926
24 W Fulton, Intersection theory, 2, Springer (1984) MR0732620
25 C Haase, G Musiker, J Yu, Linear systems on tropical curves, Math. Z. 270 (2012) 1111 MR2892941
26 J Harris, I Morrison, Slopes of effective divisors on the moduli space of stable curves, Invent. Math. 99 (1990) 321 MR1031904
27 J Harris, D Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982) 23 MR0664324
28 J Harris, L Tu, Chern numbers of kernel and cokernel bundles, Invent. Math. 75 (1984) 467 MR0735336
29 R Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980) 121 MR0597077
30 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
31 D Jensen, S Payne, Tropical independence, II : The maximal rank conjecture for quadrics, Algebra Number Theory 10 (2016) 1601 MR3556794
32 D Khosla, Tautological classes on moduli spaces of curves with linear series and a push-forward formula when ρ = 0, preprint (2007) arXiv:0704.1340
33 H Lange, M S Narasimhan, Maximal subbundles of rank two vector bundles on curves, Math. Ann. 266 (1983) 55 MR0722927
34 H Lange, P E Newstead, S S Park, Nonemptiness of Brill–Noether loci in M(2,K), Comm. Algebra 44 (2016) 746 MR3449951
35 R Lazarsfeld, Brill–Noether–Petri without degenerations, J. Differential Geom. 23 (1986) 299 MR0852158
36 A Logan, The Kodaira dimension of moduli spaces of curves with marked points, Amer. J. Math. 125 (2003) 105 MR1953519
37 S Mukai, Curves, K3 surfaces and Fano 3–folds of genus 10, from: "Algebraic geometry and commutative algebra, I" (editors H Hijikata, H Hironaka, M Maruyama, H Matsumura, M Miyanishi, T Oda, K Ueno), Kinokuniya (1988) 357 MR0977768
38 S Mukai, Noncommutativizability of Brill–Noether theory and 3–dimensional Fano varieties, Sūgaku 49 (1997) 1 MR1478148
39 M Nagata, On self-intersection number of a section on a ruled surface, Nagoya Math. J. 37 (1970) 191 MR0258829
40 P E Newstead, Characteristic classes of stable bundles of rank 2 over an algebraic curve, Trans. Amer. Math. Soc. 169 (1972) 337 MR0316452
41 M Raynaud, Sections des fibrés vectoriels sur une courbe, Bull. Soc. Math. France 110 (1982) 103 MR0662131
42 X Sun, Moduli spaces of SL(r)–bundles on singular irreducible curves, Asian J. Math. 7 (2003) 609 MR2074894
43 S L Tan, On the slopes of the moduli spaces of curves, Internat. J. Math. 9 (1998) 119 MR1612259
44 M Teixidor i Bigas, Rank two vector bundles with canonical determinant, Math. Nachr. 265 (2004) 100 MR2033069
45 M Teixidor i Bigas, Petri map for rank two bundles with canonical determinant, Compos. Math. 144 (2008) 705 MR2422346
46 M Thaddeus, Conformal field theory and the cohomology of the moduli space of stable bundles, J. Differential Geom. 35 (1992) 131 MR1152228
47 A Verra, The unirationality of the moduli spaces of curves of genus 14 or lower, Compos. Math. 141 (2005) 1425 MR2188443
48 C Voisin, Sur l’application de Wahl des courbes satisfaisant la condition de Brill–Noether–Petri, Acta Math. 168 (1992) 249 MR1161267
49 N Zhang, Towards the Bertram–Feinberg–Mukai conjecture, J. Pure Appl. Algebra 220 (2016) 1588 MR3423466