Scrollar invariants, syzygies and representations of the symmetric group

References

[1] E. Ballico, A remark on linear series on general k-gonal curves, Boll. Unione Mat. Ital. A (7) 3 (1989), no. 2, 195–197. Search in Google Scholar

[2] K. Behnke, On projective resolutions of Frobenius algebras and Gorenstein rings, Math. Ann. 257 (1981), no. 2, 219–238. 10.1007/BF01458286Search in Google Scholar

[3] M. Bhargava, Higher composition laws. III. The parametrization of quartic rings, Ann. of Math. (2) 159 (2004), no. 3, 1329–1360. 10.4007/annals.2004.159.1329Search in Google Scholar

[4] M. Bhargava, Higher composition laws. IV. The parametrization of quintic rings, Ann. of Math. (2) 167 (2008), no. 1, 53–94. 10.4007/annals.2008.167.53Search in Google Scholar

[5] C. Bopp and M. Hoff, Resolutions of general canonical curves on rational normal scrolls, Arch. Math. (Basel) 105 (2015), no. 3, 239–249. 10.1007/s00013-015-0794-xSearch in Google Scholar

[6] G. Bujokas and A. P. Patel, Invariants of a general branched cover of P 1 , Int. Math. Res. Not. IMRN 2021 (2021), no. 6, 4564–4604. 10.1093/imrn/rnaa156Search in Google Scholar

[7] G. Casnati, Covers of algebraic varieties. III. The discriminant of a cover of degree 4 and the trigonal construction, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1359–1378. 10.1090/S0002-9947-98-02136-9Search in Google Scholar

[8] G. Casnati and T. Ekedahl, Covers of algebraic varieties. I. A general structure theorem, covers of degree 3 , 4 and Enriques surfaces, J. Algebraic Geom. 5 (1996), no. 3, 439–460. Search in Google Scholar

[9] W. Castryck and F. Cools, Linear pencils encoded in the Newton polygon, Int. Math. Res. Not. IMRN 2017 (2017), no. 10, 2998–3049. 10.1093/imrn/rnw082Search in Google Scholar

[10] W. Castryck and F. Vermeulen, Lifting low-gonal curves for use in Tuitman’s algorithm, ANTS XIV—Proceedings of the Fourteenth Algorithmic Number Theory Symposium, Open Book Ser. 4, MSP, Berkeley (2020), 109–125. 10.2140/obs.2020.4.109Search in Google Scholar

[11] M. Coppens, Existence of pencils with prescribed scrollar invariants of some general type, Osaka J. Math. 36 (1999), no. 4, 1049–1057. Search in Google Scholar

[12] M. Coppens, C. Keem and G. Martens, Primitive linear series on curves, Manuscripta Math. 77 (1992), no. 2–3, 237–264. 10.1007/BF02567056Search in Google Scholar

[13] M. Coppens and G. Martens, Linear series on a general k-gonal curve, Abh. Math. Semin. Univ. Hambg. 69 (1999), 347–371. 10.1007/BF02940885Search in Google Scholar

[14] D. A. Cox, Galois theory, Pure Appl. Math. (New York), Wiley-Interscience, Hoboken 2012. 10.1002/9781118218457Search in Google Scholar

[15] A. Deopurkar and A. P. Patel, The Picard rank conjecture for the Hurwitz spaces of degree up to five, Algebra Number Theory 9 (2015), no. 2, 459–492. 10.2140/ant.2015.9.459Search in Google Scholar

[16] A. Deopurkar and A. P. Patel, Vector bundles and finite covers, Forum Math. Sigma 10 (2022), Paper No. e40. 10.1017/fms.2022.19Search in Google Scholar

[17] D. Eisenbud, N. Elkies, J. Harris and R. Speiser, On the Hurwitz scheme and its monodromy, Compos. Math. 77 (1991), no. 1, 95–117. Search in Google Scholar

[18] D. Eisenbud and J. Harris, On varieties of minimal degree (a centennial account), Algebraic geometry, Proc. Sympos. Pure Math. 46, American Mathematical Society, Providence (1987), 3–13. 10.1090/pspum/046.1/927946Search in Google Scholar

[19] W. Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math. (2) 90 (1969), 542–575. 10.2307/1970748Search in Google Scholar

[20] W. Fulton and J. Harris, Representation theory: A first course, Grad. Texts in Math. 129, Springer, New York 1991. Search in Google Scholar

[21] M. Hamermesh, Group theory and its application to physical problems, Addison-Wesley, London 1962. 10.1119/1.1941790Search in Google Scholar

[22] F. Hess, Computing Riemann–Roch spaces in algebraic function fields and related topics, J. Symbolic Comput. 33 (2002), no. 4, 425–445. 10.1006/jsco.2001.0513Search in Google Scholar

[23] F. Hess, Algorithmics of function fields, Commented slides for the UNCG Summer School in computational number theory: Function fields, 2016. Search in Google Scholar

[24] F. Hivert and N. M. Thiéry, Deformation of symmetric functions and the rational Steenrod algebra, Invariant theory in all characteristics, CRM Proc. Lecture Notes 35, American Mathematical Society, Providence (2004), 91–125. 10.1090/crmp/035/06Search in Google Scholar

[25] A. Landesman and D. Litt, Applications of the algebraic geometry of the Putman–Wieland conjecture, preprint (2022), https://arxiv.org/abs/2209.00718. Search in Google Scholar

[26] A. Landesman and D. Litt, Geometric local systems on very general curves and isomonodromy, preprint (2022), https://arxiv.org/abs/2202.00039. Search in Google Scholar

[27] A. Landesman, R. Vakil and M. M. Wood, Low degree Hurwitz stacks in the Grothendieck ring, preprint (2022), https://arxiv.org/pdf/2203.01840. Search in Google Scholar

[28] H. W. Lenstra, Jr., J. Pila and C. Pomerance, A hyperelliptic smoothness test. II, Proc. Lond. Math. Soc. (3) 84 (2002), no. 1, 105–146. 10.1112/plms/84.1.105Search in Google Scholar

[29] V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), no. 3, 205–239. 10.1007/BF01420526Search in Google Scholar

[30] J. Neukirch, Algebraic number theory, Grundlehren Math. Wiss. 322, Springer, Berlin 1999. 10.1007/978-3-662-03983-0Search in Google Scholar

[31] A. P. Patel, The geometry of Hurwitz space, Ph.D. thesis, Harvard University, 2013. Search in Google Scholar

[32] S. Recillas, Jacobians of curves with g 4 1 ’s are the Prym’s of trigonal curves, Bol. Soc. Mat. Mex. (2) 19 (1974), no. 1, 9–13. Search in Google Scholar

[33] B. E. Sagan, The symmetric group. Representations, combinatorial algorithms, and symmetric functions, Springer, New York 2001. 10.1007/978-1-4757-6804-6_3Search in Google Scholar

[34] F.-O. Schreyer, Syzygies of canonical curves and special linear series, Math. Ann. 275 (1986), no. 1, 105–137. 10.1007/BF01458587Search in Google Scholar

[35] F.-O. Schreyer and F. Tanturri, Matrix factorizations and curves in ℙ 4 , Doc. Math. 23 (2018), 1895–1924. 10.4171/dm/663Search in Google Scholar

[36] J.-P. Serre, Linear representations of finite groups, Grad. Texts in Math. 42, Springer, New York 1977. 10.1007/978-1-4684-9458-7Search in Google Scholar

[37] P. Solomatin, Global fields and their L-functions, Ph.D. thesis, Leiden University, 2021. Search in Google Scholar

[38] B. L. van der Waerden, Die Zerlegungs-und Trägheitsgruppe als Permutationsgruppen, Math. Ann. 111 (1935), no. 1, 731–733. 10.1007/BF01472249Search in Google Scholar

[39] B. van Geemen, Some remarks on Brauer groups of K ⁢ 3 surfaces, Adv. Math. 197 (2005), no. 1, 222–247. 10.1016/j.aim.2004.10.004Search in Google Scholar

[40] F. Vermeulen, Lifting curves of low gonality, Master’s thesis, KU Leuven, 2019. Search in Google Scholar

[41] F. Vermeulen, Arithmetically equivalent number fields have approximately the same successive minima, preprint (2022), https://arxiv.org/abs/2206.13855v2. Search in Google Scholar

[42] K. H. Wilson, Three perspectives on n points in ℙ n - 2 , Ph.D. thesis, Princeton University, 2013. Search in Google Scholar