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Some remarks on Landau-Ginzburg potentials for odd-dimensional quadrics [article]

Vassily Gorbounov, Maxim Smirnov
2013 arXiv   pre-print
cohomology of these quadrics.  ...  Namely, we show that the initial conditions of the quantum cohomology Frobenius manifold of the quadric can be obtained from the suitably modified standard Landau-Ginzburg model.  ...  Some part of this work was done while the second author visited the IHES, Paris whose hospitality is gratefully acknowledged.  ... 
arXiv:1304.0142v2 fatcat:mpfj5hrhnjebzp6oyznzyrhgii

SOME REMARKS ON LANDAU–GINZBURG POTENTIALS FOR ODD-DIMENSIONAL QUADRICS

VASSILY GORBOUNOV, MAXIM SMIRNOV
2014 Glasgow Mathematical Journal  
Namely, we show that the initial conditions of the quantum cohomology Frobenius manifold of the quadric can be obtained from the suitably modified standard Landau–Ginzburg model.  ...  possibility of constructing a Frobenius manifold for the standard Landau–Ginzburg model of odd-dimensional quadricsQ2n+1and matching it with the Frobenius manifold attached to the quantum cohomology of these quadrics  ...  In fact, all the results hold for an arbitrary odd-dimensional quadric. REMARK. After the first version of this preprint was posted on the arxiv, an interesting preprint by C. Pech and K.  ... 
doi:10.1017/s0017089514000433 fatcat:bvmzkiigival7p2bowuubjpsle

Quadric splines

Claudia Bangert, Hartmut Prautzsch
1999 Computer Aided Geometric Design  
Surface rendering or point location on a surface can easier be accomplished in an implicit rather than parametric representation.  ...  Their construction is based on the implicit B ezier representation introduced by Sederberg 1985] and employs the idea of the Powell-Sabin split 1977] for bivariate C 1 -piecewise quadratics.  ...  Now substituting R and r for P and p in Remark 7.2 gives for i = 1 2 that R i has C 1 -contact with Q i in the plane a rb . 9 Some Remarks Remark 9.1 The map can be expressed in homogeneous coordinates  ... 
doi:10.1016/s0167-8396(98)00047-8 fatcat:kfu5uh5izjeihnqhznikxiwuda

Page 712 of American Journal of Mathematics Vol. 65, Issue 4 [page]

1943 American Journal of Mathematics  
Furthermore we remark that a certain quadric possessing many remarkable properties is defined in a simple way, and that a new property of the Darboux pencil of quadrics has been added.  ...  In the second part of this paper the equation of the osculating linear complex of every asymptotic osculating ruled surface is first determined, some new invariant quadrics are then introduced as analogues  ... 

A Remark on Quadrics in Projective Klingenberg Spaces over a Certain Local Algebra

Marek Jukl
2020 Mathematics  
This article is devoted to some polar properties of quadrics in the projective Klingenberg spaces over a local ring which is a linear algebra generated by one nilpotent element.  ...  The polarity induced by a quadric is also studied.  ...  We present some geometric interpretation of certain "algebraic" properties of quadrics and quadratic forms in such case.  ... 
doi:10.3390/math8122168 fatcat:rmy2zbjkxjca5k7vdtn76bzo4q

The Projective Theory of Surfaces in Ruled Space, I

Chenkuo Pa
1943 American Journal of Mathematics  
Furthermore we remark that a certain quadric possessing many remarkable properties is defined in a simple way, and that a new property of the Darboux pencil of quadrics has been added.  ...  In the second part of this paper the equation of the osculating linear complex of every asymptotic osculating ruled surface is first determined, some new invariant quadrics are then introduced as analogues  ... 
doi:10.2307/2371877 fatcat:22jesrzjsncmzlp34tyzberrzu

Page 120 of American Journal of Mathematics Vol. 66, Issue 1 [page]

1944 American Journal of Mathematics  
We shall conclude this paper by a remark on certain new invariant quadrics. The osculating linear complex /?  ...  It seems of some interest to give here a new characteristic property of the quadric of Lie: . . ° . , The two consecutive asymptotic osculating linear complexes R, and f, (R. and R’,) have always one and  ... 

Birational maps between Calabi–Yau manifolds associated to webs of quadrics

Mateusz Michałek
2012 Journal of Algebra  
We consider two varieties associated to a web of quadrics W in the projective space of dimension 7.  ...  One is the base locus and the second one is the double cover of the three dimensional projective space branched along the determinant surface of W.  ...  We start with general remarks concerning webs of quadrics. Proposition 1.1.  ... 
doi:10.1016/j.jalgebra.2012.07.019 fatcat:4k3bii6f7jgv5ozz2t2vamviwa

Maximality of quartic symmetroids with a double quadric of codimension 1 [article]

Martin Helsø
2019 arXiv   pre-print
In the maximal case, the quadric is reducible and consists of rank-3-points. If the quadric is irreducible, it consists of rank-2-points and the symmetroid is at most 3-dimensional.  ...  We prove that the dimension of a quartic symmetroid singular along a quadric of codimension 1 is at most 4, if it is not a cone.  ...  Some of the singularities may be real, and some of the real singularities may lie on the topological boundary of the spectrahedron.  ... 
arXiv:1905.01091v1 fatcat:qnocqqxoj5estikdzbaai7cmhq

Double quadrics with large automorphism groups

Victor Przyjalkowski, Constantin Shramov
2016 arXiv   pre-print
We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality  ...  In §2 we make some preliminary remarks about double quadrics and their automorphisms.  ...  Keeping in mind Lemma 4.1 and Remark 2.1, in the rest of this section we will ignore the case λ = − 1 5 and will denote by Q the quadric given by equation for some µ, ν ∈ C.  ... 
arXiv:1604.00307v2 fatcat:lniu6obrkjhu3cgw5jwnxw7c7m

Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties [article]

Alain Couvreur, Iwan Duursma
2012 arXiv   pre-print
We give the parameters of any evaluation code on a smooth quadric surface.  ...  For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure of these codes and using the BCH  ...  Remark 3.12. Since the Picard group of E is generated by O E (1), any evaluation code on this surface is equivalent to C E (s) for some s.  ... 
arXiv:1101.4603v3 fatcat:nuiyhnnqufallajpjyoqkkqoay

Evaluation codes from smooth quadric surfaces and twisted Segre varieties

Alain Couvreur, Iwan Duursma
2012 Designs, Codes and Cryptography  
For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure on these codes and using the BCH  ...  We give the parameters of any evaluation code on a smooth quadric surface.  ...  Remark 3.12. Since the Picard group of E is generated by O E (1), any evaluation code on this surface is equivalent to C E (s) for some s.  ... 
doi:10.1007/s10623-012-9692-4 fatcat:gdtltxakkbhjpd6xf3bxxxfrje

Intersection of two quadrics with no common hyperplane in P^n(F_q) [article]

Frédéric A. B. Edoukou, San Ling, Chaoping Xing
2009 arXiv   pre-print
Let Q_1 and Q_2 be two arbitrary quadrics with no common hyperplane in P^n(F_q). We give the best upper bound for the number of points in the intersection of these two quadrics.  ...  This result inspires us to establish the conjecture on the number of points of an algebraic set X⊂P^n(F_q) of dimension s and degree d: |X(F_q)|< dq^s+π_s-1.  ...  First of all we recall some generaties on quadrics.  ... 
arXiv:0907.4556v1 fatcat:mlqgyfvwovfuxgci7h2xb4ipdi

Notes on the Theory of Curves in the Affine Space

Buchin SU
1930 Japanese Journal of Mathematics: Transactions and Abstracts  
Journ., 31 (1929) In the following lines I will add some remarks to the geometrical interpretations of the vector the invariants k(s), t(s) and the trihedron of Winternitz.  ...  Making use of this quadric, I will further give some applications to special classes of curves. 1.  ... 
doi:10.4099/jjm1924.7.0_1 fatcat:tqepztyedvaencil7yrecte3ea

A remark on K3s of Todorov type (0,9) and (0,10) [article]

C.Madonna
2002 arXiv   pre-print
In other cases this is due to the structure of the Picard lattice and not only on its rank.  ...  This is due, in some cases, to the (too high, e.g. bigger then or equal to 12) rank of the Picard lattice as showed by Mukai in [Muk3].  ...  Let us briefly recall some generalities on Todorov lattices and K3s of Todorov type. We refer the reader to [10] or [12] for more details. Definition.  ... 
arXiv:math/0205146v1 fatcat:cxbutovqczegnifjbgikumo5ua
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