• Journal of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.683-692
• /
• 2024

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to that of the usual projective plane. Recent explicit constructions of fake projective planes embed them via their bicanonical embedding in ℙ⁹. In this paper, we study Keum's fake projective plane (a = 7, p = 2, {7}, D₃2₇) and use the equations of [1] to construct an embedding of fake projective plane in ℙ⁵. We also simplify the 84 cubic equations defining the fake projective plane in ℙ⁹.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.145-155
• /
• 2002

In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.319-335
• /
• 2011

We classify equivariant topoligical complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.141-148
• /
• 1998

In the present paper, some pinching theorems for the curvatures of the totally complex submanifolds of the Cayley projective plane $CaP^2$ are obtained.

• Journal of the Korean Mathematical Society
• /
• v.39 no.6
• /
• pp.821-879
• /
• 2002

Let U, V and W be complex vector spaces of dimensions 3, 3 and 4 respectively. The reductive algebraic group G = PGL(U) $\times$ PGL(W) $\times$ PGL(W) acts linearly on the projective tensor product space (equation omitted). In this paper, we show that the G-equivalence classes of the projective tensors are in one-to-one correspondence with the PGL(3)-equivalence classes of unordered configurations of six points on the projective plane.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.183-196
• /
• 2005

In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.27-43
• /
• 2022

The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane ℝℙ² are completely classified up to topological equivalence. A planar graph (i.e., embedded in the plane), admitting the one-sided fattening, is known to be a cactus boundary. For the graphs embedded in ℝℙ² admitting the one-sided fattening, unlike the planar graphs, a new building block appears: a bracelet along the Möbius band, which is not a connected summand of the oriented surfaces.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.461-473
• /
• 2016

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.2
• /
• pp.628-646
• /
• 2016

This paper proposes a novel channel assignment scheme that is based on finite projective plane (FPP) theory. The proposed scheme involves using a Markov chain model to allocate N channels to N users through intermixed channel group arrangements, particularly when channel resources are idle because of inefficient use. The intermixed FPP-based channel group arrangements successfully related Markov chain modeling to punch through ratio formulations proposed in this study, ensuring fair resource use among users. The simulation results for the proposed FPP scheme clearly revealed that the defined throughput increased, particularly under light traffic load conditions. Nevertheless, if the proposed scheme is combined with successive interference cancellation techniques, considerably higher throughput is predicted, even under heavy traffic load conditions.

• Review of KIISC
• /
• v.2 no.4
• /
• pp.17-29
• /
• 1992

본 논문에서는 시스템 내의 모든sote들에게 분산되어 있는 정보들을 수렴하여 일치를 이루고, 그 결과를 모든 site들이 알도록 하는 다중 일치 프로토콜을 위한 효과적인 통신 방법을 제안하고자 한다. 분산 시스템에 참여하는 computer 또는 site들의 수를 N이라 할때, $O(N^2)$의 message를 필요로하면서 한 round안에 일치를 이룰 수 있는 프로토콜은 message의 수가 너무 많다는 것이 단점이다. 이에 본 논문에서는 Finite Projective Planes을 이용하여 message의 수를 줄이면서 두 round 안에 일치를 이룰 수 있는 통신 방법을 제안한다. 이때, 각 round마다 필요한 message의 수는 O(N$)이다. 또한, 이 통신 방법에서 이용되는 Finite Projective Planes을 구축하는 알고리즘을 제안하고자한다.