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Computing the Chow variety of quadratic space curves [article]

Peter Bürgisser, Kathlén Kohn, Pierre Lairez, Bernd Sturmfels
2015 arXiv   pre-print
Following Gel'fand, Kapranov and Zelevinsky, it decomposes into Chow forms of plane conics, Chow forms of pairs of lines, and Hurwitz forms of quadric surfaces. We compute the ideals of these loci.  ...  Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces.  ...  Introduction The Chow variety, introduced in 1937 by Chow and van der Waerden [4] , parameterizes algebraic cycles of any fixed dimension and degree in a projective space, each given by its Chow form.  ... 
arXiv:1508.07219v2 fatcat:manafoaug5hr7kmzf5gyggkjyi

Computing the Chow Variety of Quadratic Space Curves [chapter]

Peter Bürgisser, Kathlén Kohn, Pierre Lairez, Bernd Sturmfels
2016 Lecture Notes in Computer Science  
Following Gel'fand, Kapranov and Zelevinsky, it decomposes into Chow forms of plane conics, Chow forms of pairs of lines, and Hurwitz forms of quadric surfaces. We compute the ideals of these loci.  ...  Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces.  ...  Introduction The Chow variety, introduced in 1937 by Chow and van der Waerden [4] , parameterizes algebraic cycles of any fixed dimension and degree in a projective space, each given by its Chow form.  ... 
doi:10.1007/978-3-319-32859-1_10 fatcat:g7b2fo7p7bakfnqehanr25xyb4

The Chow Ring of the Hilbert Scheme of Rational Normal Curves [article]

R. Pandharipande
1996 arXiv   pre-print
Let H(d) be the (open) Hilbert scheme of rational normal curves of degree d in P^d. A presentation of the integral Chow ring of H(d) is given via equivariant Chow ring computations.  ...  Included also in the paper are algebraic computations of the integral equivariant Chow rings of the algebraic groups O(n), SO(2k+1).  ...  Let A * (d) be the integral Chow ring of H(d). In case d = 1, there is a unique rational normal curve in P 1 . Hence, H(1) is a point. H(2) is the space of nonsingular plane conics.  ... 
arXiv:alg-geom/9607025v1 fatcat:ljhftpmltbgcjitesg26kkhzde

Page 115 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
For example, if X is the projective line, then S"X is isomorphic to projective n-space, and ,, is the inclusion of a hyperplane; the Chow homology is the divided powers algebra in one variable, and the  ...  In the case of curves, the authors also construct a bijective “Fourier transform” from Chow homology to Chow cohomology, sending the Pontryagin product to the intersection product and respecting the induced  ... 

Page 6894 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
description of the tautological ring of the moduli space of curves.  ...  (English summary) Moduli of curves and abelian varieties, 109-129, Aspects Math., £33, Vieweg, Braunschweig, 1999. Let #, denote the moduli space of smooth curves of genus g > 2.  ... 

Page 847 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Following work of a number of papers for g = 2,3,4, the author studies the Chow ring A,(s) of the moduli space of curves of genus five.  ...  Montserrat Teixidor i Bigas (Cambridge) 97b:14029 14H10 14C17 Izadi, E. (1-HRV; Cambridge, MA) The Chow ring of the moduli space of curves of genus 5.  ... 

Page 8704 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Motivated by the theory of error-correcting codes, the authors give an algorithm for computing a basis for the linear space /(D) associated with a divisor D on an algebraic curve over a perfect field.  ...  Here My is the va- riety of lines on the variety Y = Y(F) =P'°nS' cP), where P'° is a linear space depending on F, S'° is a spinor variety of isotropic P*’s in an 8-dimensional smooth quadric Q* c P’,  ... 

A General Framework for Trajectory Triangulation

Jeremy Yirmeyahu Kaminski, Mina Teicher
2004 Journal of Mathematical Imaging and Vision  
The first case is based on a new representation (to computer vision) of curves (trajectories) where a curve is represented by a family of hypersurfaces in the projective space P 5 .  ...  The triangulation of linear trajectories is now well handled. The case of quadratic trajectories also received some attention.  ...  The intersection of any family of varieties is a variety. The empty set and the whole space are varieties. Then the varieties are the closed sets of a topology called the Zariski topology.  ... 
doi:10.1023/b:jmiv.0000026555.79056.b8 fatcat:h4xkcyuwb5atpos67sv2l5s5zm

Implicit representations of high-codimension varieties

Ioannis Z. Emiris, Christos Konaxis, Clément Laroche
2019 Computer Aided Geometric Design  
Our second, and main contribution is an implicitization method of parametric space curves and varieties of codimension > 1, which exploits the theory of Chow forms to obtain the equations of conical (hyper  ...  In this paper we shift the focus on space curves and, more generally, on varieties of codimension larger than 1, and discuss approaches that are not sensitive to base points.  ...  In particular, we avoid the explicit computation of the Chow form and instead focus on a proper subset of the Chow variety that is enough to describe the space curve.  ... 
doi:10.1016/j.cagd.2019.07.003 fatcat:wpu5m42k4rckdj77kclvlgyqpu

Page 702 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
He formulates a problem of describing vector bundles for quadratic periods over the Bers fibre space and over Teichmiiller space, in terms of vector bundles that are already well known.  ...  {For the entire collection see MR 88j:14002.} James D. Lewis (3-SK) 14 ALGEBRAIC GEOMETRY 89b:14012 14C40 14C17 14L30 Vistoli, Angelo (1-MIT) Chow groups of quotient varieties. J.  ... 

Page 2667 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
(F-NICE; Nice) On Chow rings of fine moduli spaces of modules. J. Reine Angew. Math. 461 (1995), 179-187.  ...  The computations are done for the following cases: the Hilbert scheme of 1 points of a smooth projective surface and the higher order Kummer varieties of a two-dimensional abelian variety over C or of  ... 

Page 1267 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
The proof consists of bounding the dimension of the tangent space to M at a suitable point using the description by quadratic differentials and interpreting the endomorphisms via linear sub- systems of  ...  Philippon also defined a notion of height for projective varieties, based on its Chow form. The fi- nal section of the paper proves a formula relating Philippon’s and Faltings’ heights.  ... 

Determinantal representations of the cubic discriminant [article]

Dominic Bunnett, Hanieh Keneshlou
2019 arXiv   pre-print
The first representation is the Chow form of the 2-uple embedding of P^3 and is computed as the Pfaffian of the Chow form of a rank 2 Ulrich bundle on this Veronese variety.  ...  We compute and study two determinantal representations of the discriminant of a cubic quaternary form.  ...  We would also like to thank the anonymous referee whose comments improved the clarity of the material.  ... 
arXiv:1909.05579v3 fatcat:bxzlntgn5nhupkjojjsha5r4x4

Equivariant Chow-Witt groups and moduli stacks of elliptic curves [article]

Andrea Di Lorenzo, Lorenzo Mantovani
2021 arXiv   pre-print
We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new generators.  ...  Along the way, we also determine the Chow-Witt ring of the classifying stack of μ_2n.  ...  In addition the second named author wishes to sincerely thank M. Wendt for the huge influence on his understanding of the subject of this paper. The second named author also thanks J.  ... 
arXiv:2107.02305v1 fatcat:2mijxyyfmfebdl7fwpjflba4zq

Homotopy invariants for ℳ_0,n via Koszul duality [article]

Vladimir Dotsenko
2020 arXiv   pre-print
We show that the integral cohomology rings of the moduli spaces of stable rational marked curves are Koszul. This answers an open question of Manin.  ...  Using the machinery of Koszul spaces developed by Berglund, we compute the rational homotopy Lie algebras of those spaces, and obtain some estimates for Betti numbers of their free loop spaces in case  ...  APPLICATION TO HOMOTOPY INVARIANTS OF LOOP SPACES Let us discuss some applications of our result to computation of homotopy invariants of loop spaces of moduli spaces of stable curves.  ... 
arXiv:1902.06318v3 fatcat:urkjxof5kvchnbu3g676zhdsgi
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