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Chow quotients of Grassmannian I
[article]
1992
arXiv
pre-print
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We study in detail the closures of the torus orbits 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. ...
arXiv:alg-geom/9210002v1
fatcat:ctwb7ggxajf5bkxhoovimaftpa
The geometry of some two-character sets
2007
Designs, Codes and Cryptography
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A projective (n, d, w 1 , w 2 ) q 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. ...
doi:10.1007/s10623-007-9155-5
fatcat:2qtqopwfxnaijjmm7kugfkujzq
A tropical approach to secant dimensions
2008
Journal of Pure and Applied Algebra
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; 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. ...
doi:10.1016/j.jpaa.2007.05.022
fatcat:2r63ybtiuzdqjablixn46jjhr4
Flexible affine cones and flexible coverings
[article]
2016
arXiv
pre-print
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We apply this criterion to prove flexibility of affine cones over secant varieties of Segre--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). ...
arXiv:1612.01144v1
fatcat:cpb4vefccrhfbjnwhcdrk7sagi
Page 4246 of Mathematical Reviews Vol. , Issue 2002F
[page]
2002
Mathematical Reviews
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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. ...
Statistics of linear families of smooth functions on knots
[article]
2010
arXiv
pre-print
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invariant of K 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). ...
arXiv:1006.1267v2
fatcat:4ndzhof5hrglhcjrk2ddh5jzki
Flexible affine cones and flexible coverings
2018
Mathematische Zeitschrift
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We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-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. ...
doi:10.1007/s00209-018-2069-2
fatcat:dbn2geie2fcyzf2ok2foki7uze
The critical space for orthogonally invariant varieties
[article]
2021
arXiv
pre-print
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This construction applies to singular t-ples for tensors 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 ...
arXiv:2104.14998v1
fatcat:nihq5wn2srhq3lki7j5fmidqze
Page 4179 of Mathematical Reviews Vol. , Issue 82j
[page]
1982
Mathematical Reviews
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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. ...
Octonionic Planes and Real Forms of G2, F4 and E6
[article]
2022
arXiv
pre-print
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In this work we present a useful way to introduce the octonionic projective 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. ...
arXiv:2203.02671v1
fatcat:jsmh2qzcmnbwnh4kfw2es7bpra
The Rough Veronese variety
[article]
2018
arXiv
pre-print
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Their signature variety shows surprising analogies with the 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. ...
arXiv:1809.02522v2
fatcat:imlc52mjyvarroefkfg6kub3w4
Page 4097 of Mathematical Reviews Vol. , Issue 2003f
[page]
2003
Mathematical Reviews
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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 ...
Page 1573 of Mathematical Reviews Vol. 58, Issue 3
[page]
1979
Mathematical Reviews
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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. ...
The Picard Group of Brauer-Severi Varieties
[article]
2017
arXiv
pre-print
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Now, by Lemma 6.4 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 . ...
arXiv:1706.10093v1
fatcat:zi3wpomk65ckdg3aqjccqlnrvy
A tropical approach to secant dimensions
[article]
2006
arXiv
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; this proof might be generalisable to cover all 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 ...
arXiv:math/0605345v3
fatcat:iomubj7ryzcn7fcsemmlsthuau
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