Multigraded Castelnuovo–Mumford regularity via Klyachko filtrations

References

[1] A. Aramova, K. Crona and E. De Negri, Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions, J. Pure Appl. Algebra 150 (2000), no. 3, 215–235. 10.1016/S0022-4049(99)00100-0Search in Google Scholar

[2] V. V. Batyrev, On the classification of smooth projective toric varieties, Tohoku Math. J. (2) 43 (1991), no. 4, 569–585. 10.2748/tmj/1178227429Search in Google Scholar

[3] V. V. Batyrev and D. A. Cox, On the Hodge structure of projective hypersurfaces in toric varieties, Duke Math. J. 75 (1994), no. 2, 293–338. 10.1215/S0012-7094-94-07509-1Search in Google Scholar

[4] A. M. Bigatti, Computation of Hilbert–Poincaré series, J. Pure Appl. Algebra 119 (1997), no. 3, 237–253. 10.1016/S0022-4049(96)00035-7Search in Google Scholar

[5] N. Botbol and M. Chardin, Castelnuovo Mumford regularity with respect to multigraded ideals, J. Algebra 474 (2017), 361–392. 10.1016/j.jalgebra.2016.11.017Search in Google Scholar

[6] M. Chardin and N. Nemati, Multigraded regularity of complete intersections, preprint (2020), https://arxiv.org/abs/2012.14899. Search in Google Scholar

[7] D. A. Cox, J. B. Little and H. K. Schenck, Toric Varieties, Grad. Stud. Math. 124, American Mathematical Society, Providence, 2011. 10.1090/gsm/124Search in Google Scholar

[8] K. Crona, Standard bigraded Hilbert functions, Comm. Algebra 34 (2006), no. 2, 425–462. 10.1080/00927870500387358Search in Google Scholar

[9] D. Eisenbud, M. Mustaţǎ and M. Stillman, Cohomology on toric varieties and local cohomology with monomial supports, J. Symbolic Comput. 29 (2000), 583–600. 10.1006/jsco.1999.0326Search in Google Scholar

[10] D. R. Grayson and M. E. Stillman, Macaulay2, a software system for research in algebraic geometry, http://www.math.uiuc.edu/Macaulay2/. Search in Google Scholar

[11] M. Hering, M. Mustaţă and S. Payne, Positivity properties of toric vector bundles, Ann. Inst. Fourier (Grenoble) 60 (2010), no. 2, 607–640. 10.5802/aif.2534Search in Google Scholar

[12] L. T. Hoa and E. Hyry, On local cohomology and Hilbert function of powers of ideals, Manuscripta Math. 112 (2003), no. 1, 77–92. 10.1007/s00229-003-0393-1Search in Google Scholar

[13] N. D. Hoang and N. V. Trung, Hilbert polynomials of non-standard bigraded algebras, Math. Z. 245 (2003), no. 2, 309–334. 10.1007/s00209-003-0546-7Search in Google Scholar

[14] A. A. Klyachko, Equivariant bundles on toral varieties, Izv. Akad. Nauk SSSR Ser. Mat. 539 (1989), no. 5, 1001–1039. 10.1070/IM1990v035n02ABEH000707Search in Google Scholar

[15] A. A. Klyachko, Vector bundles and torsion free sheaves on the projective plane, preprint (1991). Search in Google Scholar

[16] D. Maclagan and G. G. Smith, Multigraded Castelnuovo–Mumford regularity, J. Reine Angew. Math. 571 (2004), 179–212. 10.1515/crll.2004.040Search in Google Scholar

[17] D. Maclagan and G. G. Smith, Uniform bounds on multigraded regularity, J. Algebraic Geom. 14 (2005), no. 1, 137–164. 10.1090/S1056-3911-04-00385-6Search in Google Scholar

[18] R. M. Miró-Roig and M. Salat Moltó, Klyachko decomposition of monomial ideals, preprint. Search in Google Scholar

[19] S. Payne, Moduli of toric vector bundles, Compos. Math. 144 (2008), no. 5, 1199–1213. 10.1112/S0010437X08003461Search in Google Scholar

[20] M. Perling, Resolutions and moduli for equivariant sheaves over toric varieties, PhD thesis, Universität Kaiserslautern, 2003. 10.1002/mana.200310130Search in Google Scholar

[21] M. Şahin and I. Soprunov, Multigraded Hilbert functions and toric complete intersection codes, J. Algebra 459 (2016), 446–467. 10.1016/j.jalgebra.2016.04.013Search in Google Scholar

[22] A. Schrijver, Theory of Linear and Integer Programming, John Wiley & Sons, Chichester, 1986. Search in Google Scholar

[23] N. V. Trung and J. K. Verma, Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications, J. Commut. Algebra 2 (2010), no. 4, 515–565. 10.1216/JCA-2010-2-4-515Search in Google Scholar

[24] T. N. Trung, Regularity index of Hilbert functions of powers of ideals, Proc. Amer. Math. Soc. 137 (2009), no. 7, 2169–2174. 10.1090/S0002-9939-09-09640-3Search in Google Scholar