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Chow quotients of Grassmannian I [article]

M.Kapranov
1992 arXiv   pre-print
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

Antonio Cossidente, Nicola Durante, Giuseppe Marino, Tim Penttila, Alessandro Siciliano
2007 Designs, Codes and Cryptography  
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

Jan Draisma
2008 Journal of Pure and Applied Algebra  
; 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]

Matheusz Michałek, Alexander Perepechko, Hendrik Süß
2016 arXiv   pre-print
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  
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]

Liviu I. Nicolaescu
2010 arXiv   pre-print
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

Mateusz Michałek, Alexander Perepechko, Hendrik Süß
2018 Mathematische Zeitschrift  
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]

Giorgio Ottaviani
2021 arXiv   pre-print
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  
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]

Daniele Corradetti, Alessio Marrani, David Chester, Raymond Aschheim
2022 arXiv   pre-print
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]

Francesco Galuppi
2018 arXiv   pre-print
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  
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  
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]

Eslam Badr, Francesc Bars, Elisa Lorenzo Garcia
2017 arXiv   pre-print
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]

Jan Draisma
2006 arXiv   pre-print
; 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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