Uniqueness of the projective plane with $57$ points

Exceptional Points of an Endomorphism of the Projective Plane

Ideals of Six General Fat Points on the Projective Plane

Let X be the blowup of P 2 at six general points p 1 ; : : :; p 6 and let L X be the total transform of a line on P 2. We show that the natural multiplication map ? L)) has maximal rank for any numerically eeective divisor F on X. This fact implicitly allows determination of minimal free resolutions for ideals deening fat point subschemes Z = m 1 p 1 + + m 6 p 6 of P 2 .

The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

Real Projective Plane Mapping for Detection of Orthogonal Vanishing Points

This paper deals with the detection of orthogonal vanishing points in the Manhattan world. We are using a modified scheme of the Cascaded Hough Transform where only one Hough space is accumulated – the space of the vanishing points. The parameterization of the VPs is based on the PClines line parameterization and it is defined as a mapping of the whole real projective plane to a finite space (t...

On the Geometry of the Hilbert Schemes of Points in the Projective Plane

We determine the nef cone and effective cone of the Hilbert scheme X[n] of points on the projective plane X = P2, characterize all the rational curves in X[n] of degree-1 with respect to some very ample line bundle, describe the moduli spaces of these curves, and study the contraction of the extremal ray on X[n]. Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong Department o...