REMARKS ON SYZYGIES OF THE SECTION MODULES AND GEOMETRY OF PROJECTIVE VARIETIES

Title
REMARKS ON SYZYGIES OF THE SECTION MODULES AND GEOMETRY OF PROJECTIVE VARIETIES
Author(s)
최영욱강병련[강병련]곽시종[곽시종]
Keywords
INNER PROJECTIONS; LINEAR SYZYGIES; CASTELNUOVO; EQUATIONS; SURFACES; CURVES
Issue Date
201107
Publisher
TAYLOR & FRANCIS INC
Citation
COMMUNICATIONS IN ALGEBRA, v.39, no.7, pp.2519 - 2531
Abstract
Let X subset of P(H(0)(L)) be a smooth projective variety embedded by the complete linear system associated to a very ample line bundle L on X. We call R(L) = circle plus(l is an element of Z) H(0)(X, L(l)) the section module of L. It has been known that the syzygies of R(L) as R = Sym(H(0)(L))-module play important roles in understanding geometric properties of X [2, 3, 5, 9, 10] even if X is not projectively normal. Generalizing the case of N(2,p) [2, 10], we prove some uniform theorems on higher normality and syzygies of a given linearly normal variety X and general inner projections when R(L) satisfies property N(3,p) (Theorems 1.1, 1.2, and Proposition 3.1). In particular, our uniform bounds are sharp as hyperelliptic curves and elementary transforms of elliptic ruled surfaces show.
URI
http://hdl.handle.net/YU.REPOSITORY/24907http://dx.doi.org/10.1080/00927872.2010.491100
ISSN
0092-7872
Appears in Collections:
사범대학 > 수학교육과 > Articles
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