Sijong Kwak

Generic projections, the equations defining projective varieties and Castelnuovo regularity

Abstract. For a reduced, irreducible projective variety X of degree d and codimension e in

Smooth threefolds in

\mathbb{P}^N

{\Bbb P}^5

the Castelnuovo-Mumford regularity

without apparent triple or quadruple points and a quadruple-point formula

{\rm reg} X

Smooth projective varieties with extremal or next to extremal curvilinear secant subspaces

is defined as the least k such that X is k-regular, i.e.,

Projections of Projective Curves with Higher Linear Syzygies

H^i(\mathbb{P}^N,\mathcal{I}_X(k-i))= 0

Remarks on the Defining Equations of Smooth Threefolds in P5

for

Geometric properties of projective manifolds of small degree

i\ge1

Sharp bounds for higher linear syzygies and classifications of projective varieties

, where

Remarks on Syzygies of the Section Modules and Geometry of Projective Varieties

\mathcal {I}_X\subset\Cal O_{\mathbb{P}^N}