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ON THE EQUATIONS DEFINING SOME CURVES OF MAXIMAL REGULARITY IN P5
이완석,Shuailing Yang 영남수학회 2022 East Asian mathematical journal Vol.38 No.3
For a nondegenerate projective variety, it is a classical problem to study its defining equations with respect to a given embedding. In this paper, we precisely determine minimal sets of generators of the defining ideals of some curves of maximal regularity in $\P^5$.
Some rational curves of maximal genus in $\mathbb{P}^3$
이완석,Shuailing Yang 영남수학회 2024 East Asian mathematical journal Vol.40 No.1
For a reduced, irreducible and nondegenerate curve $C \subset \P^r$ of degree $d$, it was shown that the arithmetic genus $g$ of $C$ has an upper bound $\pi_0(d,r)$ by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll $S(0,2) \subset \P^3$ which attain the maximal arithmetic genus.
DEFINING EQUATIONS OF RATIONAL CURVES IN SMOOTH QUADRIC SURFACE
LEE, Wanseok,Yang, Shuailing The Youngnam Mathematical Society 2018 East Asian mathematical journal Vol.34 No.1
For a nondegenerate irreducible projective variety, it is a classical problem to study the defining equations of a variety with respect to the given embedding. In this paper we precisely determine the defining equations of certain types of rational curves in ${\mathbb{P}}^3$.
On the equations defining some rational curves of maximal genus in $\mathbb{P}^3$
Wanseok Lee,Shuailing Yang 영남수학회 2024 East Asian mathematical journal Vol.40 No.3
For a nondegenerate irreducible projective variety, it is a classical problem to describe its defining equations and the syzygies among them. In this paper, we precisely determine a minimal generating set and the minimal free resolution of defining ideals of some rational curves of maximal genus in $\P^3$.