Castelnuovo-Mumford regularity of Koszul cycles and Koszul homologies

Lamei, Kamran; Nemati, Navid

doi:10.1090/proc/13973

Castelnuovo-Mumford regularity of Koszul cycles and Koszul homologies
HTML articles powered by AMS MathViewer

by Kamran Lamei and Navid Nemati PDF

Proc. Amer. Math. Soc. 146 (2018), 2765-2772 Request permission

Abstract:

We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp regularity bound for the Koszul homologies of a homogeneous ideal in a polynomial ring under the same conditions.

References

Winfried Bruns, Aldo Conca, and Tim Römer, Koszul homology and syzygies of Veronese subalgebras, Math. Ann. 351 (2011), no. 4, 761–779. MR 2854112, DOI 10.1007/s00208-010-0616-1
Winfried Bruns, Aldo Conca, and Tim Römer, Koszul cycles, Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symp., vol. 6, Springer, Berlin, 2011, pp. 17–33. MR 2810423, DOI 10.1007/978-3-642-19492-4_{2}
Aldo Conca and Satoshi Murai, Regularity bounds for Koszul cycles, Proc. Amer. Math. Soc. 143 (2015), no. 2, 493–503. MR 3283639, DOI 10.1090/S0002-9939-2014-12292-1
Marc Chardin and Peter Symonds, Degree bounds on homology and a conjecture of Derksen, Compos. Math. 152 (2016), no. 10, 2041–2049. MR 3569999, DOI 10.1112/S0010437X16007430
Mark L. Green, Koszul cohomology and the geometry of projective varieties. II, J. Differential Geom. 20 (1984), no. 1, 279–289. MR 772134
David Eisenbud, Craig Huneke, and Bernd Ulrich, The regularity of Tor and graded Betti numbers, Amer. J. Math. 128 (2006), no. 3, 573–605. MR 2230917, DOI 10.1353/ajm.2006.0022
D. Grayson and M. Stillman, Macaulay2, A software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.
Giorgio Ottaviani and Raffaella Paoletti, Syzygies of Veronese embeddings, Compositio Math. 125 (2001), no. 1, 31–37. MR 1818055, DOI 10.1023/A:1002662809474
T. Vu, Fourth Veronese Embedding of Projective Spaces, Preprint (2014)