The impossibility of Fano’s configuration in a projective plane with eight points per line

The Ring of Projective Invariants of Eight Points on the Line via Representation Theory

The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular fivefold (P1)8// GL(2) is Proj(Sym•(V )/I8). We show that there is a unique cubic hypersurface S in PV whose equation s is skew-invariant, and that the singular locus of S is the modular fivefold....

an investigation of the types of text reduction in subtitling: a case study of the persian film gilaneh with english subtitles

چکیده ندارد.

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 .

Projectivities with Fixed Points on Every Line of the Plane

The system of fixed elements of a projectivity contains with any two points the line connecting them and with any two lines their intersection. It is, therefore, in its structure very much like a subplane of the plane under consideration ; and thus one may expect the structure of the projectivity to be dominated by the structure of the system of its fixed elements, provided this system is not "...