In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after Giuseppe Veronese (1854–1917). Its generalization to higher dimension is known as the Veronese variety.
The surface admits an embedding in the four-dimensional projective space defined by the projection from a general point in the five-dimensional space. Its general projection to three-dimensional projective space is called a Steiner surface.
In mathematics, the Veronesesurface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding...
simplex, hypercubic and orthoplex groups (with van Oss polytopes). A Veronesesurface in the projective plane P 5 {\displaystyle \mathbb {P} ^{5}} generalizes...
Steiner surface, that is, a 3-dimensional linear projection of the Veronesesurface. For simplicity we consider only the case r = 1. Given the sphere defined...
Paolo Caliari (1528 – 19 April 1588), known as Paolo Veronese (/ˌvɛrəˈneɪzeɪ, -zi/ VERR-ə-NAY-zay, -zee, also US: /-eɪsi/ -see, Italian: [ˈpaːolo veroˈneːze...
Unirational surfaces of characteristic 0 Veronesesurface, the Veronese embedding of the projective plane into projective 5-space White surfaces, the blow-up...
surface of degree m – 1 in Pm is either a rational normal scroll or the Veronesesurface. In projective space of dimension m + n + 1 choose two complementary...
profound. Veronesesurface Philip Ehrlich (ed) Real Numbers, Generalisations of the Reals, and Theories of Continua, 1994. Paola Cantu', Giuseppe Veronese e i...
quadrics through the canonical curve is respectively a ruled surface and a Veronesesurface. These classical results were proved over the complex numbers...
is not without a base locus. In fact each such quadric contains the Veronesesurface, which parametrizes the conics (aX + bY + cZ)2 = 0 called 'double lines'...
generalization of Bordiga surfaces. Veronesesurface An embedding of the projective plane into P5. List of algebraic surfaces Barth, Wolf P.; Hulek, Klaus;...
intersection ⋂ i H ℓ i {\displaystyle \bigcap _{i}H_{\ell _{i}}} contains the Veronesesurface Z ≃ P 2 {\displaystyle Z\simeq \mathbb {P} ^{2}} consisting of double...
List of algebraic surfaces Ruled surface Cubic surfaceVeronesesurface Del Pezzo surface Rational surface Enriques surface K3 surface Hodge index theorem...
they are more often considered as abstract varieties. For example, a Veronesesurface was not just a copy of the projective plane, but a copy of the projective...
vanishing point. It is likely that Veronese went against linear perspective due to concerns about the large surface the painting was to take up, as well...
reducible curves, then the surface is either ruled surface and in fact a scroll, or the Veronesesurface. Kronecker never published it but stated it in a...
particular that they lie on either a rational normal scroll or on the Veronesesurface. Castelnuovo, G. (1889), "Ricerche di geometria sulle curve algebriche"...
Severi showed in 1901 that the only Severi variety with n=2 is the Veronesesurface in P5. The only Severi variety with n=4 is the Segre embedding of P2×P2...
Pezzo surface is P2. Its anticanonical embedding is the degree 3 Veronese embedding into P9 using the linear system of cubics. A weak del Pezzo surface is...
since the Middle Ages and deriving from that of the homonymous town on the Veronese shore of the lake, which, together with another famous locality of the...
the watched) and the many adaptations of that painting in various media Veronese's Venus with a Mirror Artists have used mirrors to create works and to hone...
the Cenomani (550 BC). With the conquest of the Valley of the Po, the Veronese territory became Roman about 300 BC. Verona became a Roman colonia in 89...
Sanmicheli and Palladio, working with painters Titian, Tintoretto and Veronese placed him squarely among the protagonists of the art world in late 16th-century...
Italy by capacity. The stadium is named after the historic benefactor of Veronese sport, Marcantonio Bentegodi [it]. Inaugurated as a state-of-the-art facility...
contributions also from Gino Fano, Carlo Rosati, Giuseppe Torelli, Giuseppe Veronese). Elsewhere it involved H. F. Baker and Patrick du Val (UK), Arthur Byron...
been trimmed. However, by 1993, Frank Zöllner observed that the painting surface had never been trimmed; this was confirmed through a series of tests in...
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