Generic projections, the equations defining projective varieties and Castelnuovo regularity

For a reduced, irreducible projective variety X of degree d and codimension c in P-N the Castelnuovo-Mumford regularity regX is defined as the least k such that X is k-regular, i.e., H-i(P-N, I-X(k - i)) = 0 for i greater than or equal to 1, where I-X subset of O-PN is the sheaf of ideals of X. There is a long standing conjecture about k-regularity (see [5]): regX less than or equal to d - e + 1. Here we show that regX less than or equal to (d - e + 1) +10 fur any smooth fivefold and regX less than or equal to (d - e + 1) + 20 for any smooth sixfold by extending methods used in [10]. Furthermore, we give a bound for the regularity of a reduced, connected and equidimensional locally Cohen-Macaulay curve or surface in terms of degree d, codimension c and an arithmetic genus rho(a) (see Theorem 4.1).
Publisher
SPRINGER-VERLAG
Issue Date
2000-07
Language
ENG
Keywords

SMOOTH SURFACES

Citation

MATHEMATISCHE ZEITSCHRIFT, v.234, no.3, pp.413 - 434

ISSN
0025-5874
DOI
10.1007/PL00004809
URI
http://hdl.handle.net/10203/75011
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
  • Hit : 223
  • Download : 0
  • Cited 0 times in thomson ci
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡClick to seewebofscience_button
⊙ Cited 9 items in WoSClick to see citing articles inrecords_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0