• 대한수학회논문집
• /
• 제11권4호
• /
• pp.881-885
• /
• 1996

We give the optimal lower bound for the Picard number of certain surfaces in the Noether-Lefschetz locus.

• 대한수학회보
• /
• 제49권1호
• /
• pp.213-222
• /
• 2012

We determine which K3 surface with Picard number 19 is a K3 cover of an Enriques surface.

• 대한수학회지
• /
• 제53권2호
• /
• pp.433-446
• /
• 2016

We construct projective embeddings of horospherical varieties of Picard number one by means of Fano varieties of cones over rational homogeneous varieties. Then we use them to give embeddings of smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties.

• 충청수학회지
• /
• 제29권2호
• /
• pp.361-365
• /
• 2016

This note is a remark on simple observation that the degree bound of Fano (n+1)-folds of Picard number one and index greater than one can be related with that of Fano n-folds of Picard number one and index one.

• 대한수학회보
• /
• 제37권4호
• /
• pp.711-719
• /
• 2000

We generalize Gieseker\`s lemma and use it to compute Picard number of a complete intersection surface.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1427-1437
• /
• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• 대한수학회보
• /
• 제59권1호
• /
• pp.179-190
• /
• 2022

A cascade of toric log del Pezzo surfaces of Picard number one was introduced as a language of classifying all such surfaces. In this paper, we introduce a generalized concept, a semicascade of toric log del Pezzo surfaces. As applications, we discuss Kähler-Einstein toric log del Pezzo surfaces and derive a bound on the Picard number in terms of the number of singular points, generalizing some results of Dais and Suyama.

• 대한수학회지
• /
• 제46권2호
• /
• pp.237-248
• /
• 2009

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered $hyperk{\ddot{a}}hler$ manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

• 대한수학회보
• /
• 제46권5호
• /
• pp.917-930
• /
• 2009

We find all distinct representatives of isomorphism classes of genus-3 pointed trigonal curves and compute the number of isomorphism classes of a special class of genus-3 pointed trigonal curves including that of Picard curves over a finite field F of characteristic 2.

• 충청수학회지
• /
• 제22권4호
• /
• pp.689-697
• /
• 2009

We study the existence of surjective morphisms between Fano manifolds of Picard number 1, when the source is given by the intersection of a cubic hypersurface and either a quadric or another cubic hypersurface in a projective space.