Displaying similar documents to “An asymptotic higher order very ampleness theorem for blowings-up of projective spaces at general points”

On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

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Here we give several examples of projective degenerations of subvarieties of ℙ t . The more important case considered here is the d-ple Veronese embedding of ℙ n ; we will show how to degenerate it to the union of d n n-dimensional linear subspaces of ℙ t ; t : = ( n + d ) / ( n ! d ! ) - 1 and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to...

On the k-regularity of some proyective manifolds.

Alberto Alzati, Gian Mario Besana (1998)

Collectanea Mathematica

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The conjecture on the (degree-codimension + 1) - regularity of projective varieties is proved for smooth linearly normal polarized varieties (X,L) with L very ample, for low values of Delta(X,L) = degree-codimension-1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric fibrations over elliptic curves, are proved.

Homography in ℝℙ

Roland Coghetto (2016)

Formalized Mathematics

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The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7],...

Pascal’s Theorem in Real Projective Plane

Roland Coghetto (2017)

Formalized Mathematics

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In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s...

Combinatorial Grassmannians

Andrzej Owsiejczuk (2007)

Formalized Mathematics

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In the paper I construct the configuration G which is a partial linear space. It consists of k-element subsets of some base set as points and (k + 1)-element subsets as lines. The incidence is given by inclusion. I also introduce automorphisms of partial linear spaces and show that automorphisms of G are generated by permutations of the base set.

Group of Homography in Real Projective Plane

Roland Coghetto (2017)

Formalized Mathematics

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Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] “Consider in space ℝℙ2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space ℝℙ2 such that h(Pi) = Qi for i = 1, 2, 3, 4.” (Existence Statement 52 and Existence Statement 53)...