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Chow quotients of Grassmannian I
[article]

1992
*
arXiv
*
pre-print

We study in detail the closures of the torus orbits

arXiv:alg-geom/9210002v1
fatcat:ctwb7ggxajf5bkxhoovimaftpa
*and*their "visible contours" which are*Veronese*varieties in the Grassmannian. ... It is well-known that*two*subspaces L*and*L ′ lie in the same stratum (i.e. are equivalent) if*and*anly if their*sets*of bases coincide. ... Consider the 2-fold*Veronese**embedding*P k−1 ֒→ P (S 2 C k ). Then the configuration x is self-associated if*and*only if the images of of x i in the*Veronese**embedding*form a circuit. Example. ...##
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The geometry of some two-character sets

2007
*
Designs, Codes and Cryptography
*

A projective (n, d, w 1 , w 2 ) q

doi:10.1007/s10623-007-9155-5
fatcat:2qtqopwfxnaijjmm7kugfkujzq
*set*(or a*two*-*character**set*for short) is a*set*S of n points of PG(d − 1, q) with the properties that the*set*generates PG(d − 1, q)*and*that every hyperplane meets the ... Here geometric constructions of some*two*-*character**sets*are given. The constructions mainly involve commuting polarities, symplectic polarities*and*normal line-spreads of projective spaces. ... In [5] the authors constructed*two*new infinite families of*two*-*character**sets*arising from the*Veronese**embedding*of PG(2, q) with respect to the complete linear system of conics. ...##
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A tropical approach to secant dimensions

2008
*
Journal of Pure and Applied Algebra
*

;

doi:10.1016/j.jpaa.2007.05.022
fatcat:2r63ybtiuzdqjablixn46jjhr4
*and*indeed, no Segre-*Veronese**embeddings*are known where the tropical lower bound does not give the correct dimension. ... The approach is especially successful for toric varieties such as Segre-*Veronese**embeddings*. ... Acknowledgments I thank Tony Geramita, Hannah Markwig, Rick Miranda, Tim Römer, Bernd Sturmfels,*and*Seth Sullivant for their comments on earlier versions of this paper. ...##
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Flexible affine cones and flexible coverings
[article]

2016
*
arXiv
*
pre-print

We apply this criterion to prove flexibility of affine cones over secant varieties of Segre--

arXiv:1612.01144v1
fatcat:cpb4vefccrhfbjnwhcdrk7sagi
*Veronese**embeddings**and*over certain Fano threefolds. ... We would like to thank Mikhail Zaidenberg for motivating questions*and*inspiring results*and*Ivan Arzhantsev for many useful remarks*and*suggestions. ... The first author started the project under Mobilnosc+ Polish Ministry of Science program, finished under DAAD PRIME program*and*was supported by the Foundation for Polish Science (FNP). ...##
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Page 4246 of Mathematical Reviews Vol. , Issue 2002F
[page]

2002
*
Mathematical Reviews
*

n+3)/2

*and*f is locally equivalent to the second*Veronese**embedding*of CP"(c/2) into CP’ (c). ... Aledo (Albacete) 2002f:53108 53C42 53C22 Maeda, Sadahiro (J-SHIME; Matsue); Adachi, Toshiaki (J-NIT; Nagoya) A*characterization*of the second*Veronese**embedding*into a complex projective space. ...##
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Statistics of linear families of smooth functions on knots
[article]

2010
*
arXiv
*
pre-print

invariant of K

arXiv:1006.1267v2
fatcat:4ndzhof5hrglhcjrk2ddh5jzki
*and*V. ... Given a knot K in an Euclidean space E*and*a finite dimensional space V of smooth functions on K, we express the expected number of critical points of a random function in V in terms of an integral-geometric ... For any u ∈ U we*set*M u := V(u, . . . , u ℓ ). FIGURE 1 . 1 The second*Veronese**embedding*of the circle of radius 1 with center (120, 0). ...##
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Flexible affine cones and flexible coverings

2018
*
Mathematische Zeitschrift
*

We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-

doi:10.1007/s00209-018-2069-2
fatcat:dbn2geie2fcyzf2ok2foki7uze
*Veronese**embeddings**and*over certain Fano threefolds. ... We would like to thank Mikhail Zaidenberg for motivating questions*and*inspiring results*and*Ivan Arzhantsev for many useful remarks*and*suggestions. ... reproduction in any medium, provided you give appropriate credit to the original author(s)*and*the source, provide a link to the Creative Commons license,*and*indicate if changes were made. ...##
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The critical space for orthogonally invariant varieties
[article]

2021
*
arXiv
*
pre-print

This construction applies to singular t-ples for tensors

arXiv:2104.14998v1
fatcat:nihq5wn2srhq3lki7j5fmidqze
*and*to flag varieties*and*generalizes a previous result of Draisma, Tocino*and*the author. ... We have that dim(so · f ) < 3 if*and*only if f belongs to one of the following six P 3 linearly*embedded*in P(A ⊗ B ⊗ C) (each item consists of*two*P 3 's) Q A ⊗ B ⊗ C, A ⊗ Q B ⊗ C, A ⊗ B ⊗ Q C . ... The proof of Theorem 2.2 generalizes to this*setting**and*gives Since general partially symmetric tensors f have trivial isotropic groups, in the binary case X d = P 1 × . . . × P 1*embedded*in P(Sym d ...##
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Page 4179 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

Denote by C(r,,---,7,;5),°**,S,) the affine cone over the image of the Segre-

*Veronese**embedding*SV:P”" X--- xP” +—P*~' of multidegree (s,,---,s,). ... Let R*and*S be commutative rings with 1*and*X¥={X,,---,X,}, Y={Y,,---,¥,}*sets*of indeterminates. The author considers the question of when R[[ X]]=S[[Y]] implies R=S. ...##
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Octonionic Planes and Real Forms of G2, F4 and E6
[article]

2022
*
arXiv
*
pre-print

In this work we present a useful way to introduce the octonionic projective

arXiv:2203.02671v1
fatcat:jsmh2qzcmnbwnh4kfw2es7bpra
*and*hyperbolic plane through the use of*Veronese*vectors. ... Then we focus on their relation with the exceptional Jordan algebra*and*show that the*Veronese*vectors are the rank-one elements of the algebra. ... non-compact one, i.e. hyperbolic octonionic plane OH 2 , is of type (16, 0)*and**character*χ = −16; while the other*two*planes named O H 2*and*O s H 2 are of type (8, 8)*and**character*χ = 0. ...##
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The Rough Veronese variety
[article]

2018
*
arXiv
*
pre-print

Their signature variety shows surprising analogies with the

arXiv:1809.02522v2
fatcat:imlc52mjyvarroefkfg6kub3w4
*Veronese*variety,*and*our aim is to prove that this so-called Rough*Veronese*is toric. The same holds for the universal variety. ... The signatures of a given class of paths parametrize an algebraic variety inside the space of tensors,*and*these signature varieties provide both new tools to investigate paths*and*new challenging questions ... We will prove that the Rough*Veronese*variety is a toric variety,*and*we will*characterize*the monomials parameterizing it. ...##
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Page 4097 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

An example for both assertions is as follows: X is the quadratic

*Veronese**embedding*of P?”*!, Y is the image of a smooth quadric hypersurface, Z is the image of the Segre*embedding*of P! ... In this paper the author investigates the case of*two*copies of the reflection representation of S,,*and*obtains an explicit formula for the bigraded*character*of S,, acting on such harmonics from which ...##
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Page 1573 of Mathematical Reviews Vol. 58, Issue 3
[page]

1979
*
Mathematical Reviews
*

A k-arc in a projective plane 7 is a

*set*of k points no three of which are collinear; a k-arc is said to be complete if it cannot be*embedded*into a (k+1)-arc of 7. ... Let K be a k-*set*of a Galois space S,,. The*character*¢7 of K with respect to dimension d is the number of subspaces (of dimension d) of S,, which intersect K in s points. ...##
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The Picard Group of Brauer-Severi Varieties
[article]

2017
*
arXiv
*
pre-print

Now, by Lemma 6.4

arXiv:1706.10093v1
fatcat:zi3wpomk65ckdg3aqjccqlnrvy
*and*the proof of Theorem 4.2, one could construct a smooth model for the Brauer-Severi surface in P 9 k by taking the V d−3*embedding*with d = 6*and*C as in the statement. ... In this way, the natural map H 1 (k, Aut(C)) → H 1 (k, PGL g (k)), satisfies that that the image of any 1-cocycle is equivalent to a 1-cocycle with values in GL g (k),*and*recall that H 1 (k, GL g (k)) ...*Set*m = 2n+1 n*and*consider the*Veronese**embedding*Ver n : P n k ֒→ P m−1 k . ...##
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A tropical approach to secant dimensions
[article]

2006
*
arXiv
*
pre-print

; this proof might be generalisable to cover all

arXiv:math/0605345v3
fatcat:iomubj7ryzcn7fcsemmlsthuau
*Veronese**embeddings*, whose secant dimensions are known from the ground-breaking but difficult work of Alexander*and*Hirschowitz. ... In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all*Veronese**embeddings*of the projective plane except for the quadratic one*and*the quartic one are non-defective ... When X(u) is linearly independent, however, as is the case for*Veronese**and*Segre*embeddings**and*indeed for Segre products of*Veronese**embeddings*, then π is an isomorphism,*and*the bound of Proposition ...
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