Let X be a smooth variety of dimension n and degree d. There is a well-known conjecture concerning the k-regularity, saying that X is k-regular if k> d-r+n. We prove that X is k-regular if k > d-r+n+ (n-2)(n-1)/2 when n >3 (or, more generally, when X admits a general projection in P^n which is "good"), recovering the known results for curves, surfaces, threefolds (when r > 5), and improving the known results for fourfolds and higher dimensional varieties of codimension > 2.
Chiantini, L., Chianli, N., Greco, S. (2000). Bounding Castelnuovo-Mumford Regularity for Varieties with Good General Projection. JOURNAL OF PURE AND APPLIED ALGEBRA, 152(1-3), 57-64 [10.1016/S0022-4049(99)00126-7].
Bounding Castelnuovo-Mumford Regularity for Varieties with Good General Projection
Chiantini L.;
2000-01-01
Abstract
Let X be a smooth variety of dimension n and degree d. There is a well-known conjecture concerning the k-regularity, saying that X is k-regular if k> d-r+n. We prove that X is k-regular if k > d-r+n+ (n-2)(n-1)/2 when n >3 (or, more generally, when X admits a general projection in P^n which is "good"), recovering the known results for curves, surfaces, threefolds (when r > 5), and improving the known results for fourfolds and higher dimensional varieties of codimension > 2.
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https://hdl.handle.net/11365/45829
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