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

2013
*
arXiv
*
pre-print

cohomology of these

arXiv:1304.0142v2
fatcat:mpfj5hrhnjebzp6oyznzyrhgii
*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. ...##
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SOME REMARKS ON LANDAU–GINZBURG POTENTIALS FOR ODD-DIMENSIONAL QUADRICS

2014
*
Glasgow Mathematical Journal
*

Namely, we show that the initial conditions of the quantum cohomology Frobenius manifold of the

doi:10.1017/s0017089514000433
fatcat:bvmzkiigival7p2bowuubjpsle
*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. ...##
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Quadric splines

1999
*
Computer Aided Geometric Design
*

Surface rendering or point location

doi:10.1016/s0167-8396(98)00047-8
fatcat:kfu5uh5izjeihnqhznikxiwuda
*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 ...##
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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 ...##
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A Remark on Quadrics in Projective Klingenberg Spaces over a Certain Local Algebra

2020
*
Mathematics
*

This article is devoted to

doi:10.3390/math8122168
fatcat:rmy2zbjkxjca5k7vdtn76bzo4q
*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. ...##
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The Projective Theory of Surfaces in Ruled Space, I

1943
*
American Journal of Mathematics
*

Furthermore we

doi:10.2307/2371877
fatcat:22jesrzjsncmzlp34tyzberrzu
*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 ...##
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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 ...##
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Birational maps between Calabi–Yau manifolds associated to webs of quadrics

2012
*
Journal of Algebra
*

We consider two varieties associated to a web of

doi:10.1016/j.jalgebra.2012.07.019
fatcat:4k3bii6f7jgv5ozz2t2vamviwa
*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. ...##
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Maximality of quartic symmetroids with a double quadric of codimension 1
[article]

2019
*
arXiv
*
pre-print

In the maximal case, the

arXiv:1905.01091v1
fatcat:qnocqqxoj5estikdzbaai7cmhq
*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. ...##
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Double quadrics with large automorphism groups

2016
*
arXiv
*
pre-print

We classify three-dimensional nodal Fano varieties that are double covers of smooth

arXiv:1604.00307v2
fatcat:lniu6obrkjhu3cgw5jwnxw7c7m
*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. ...##
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Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties
[article]

2012
*
arXiv
*
pre-print

We give the parameters of any evaluation code

arXiv:1101.4603v3
fatcat:nuiyhnnqufallajpjyoqkkqoay
*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. ...##
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Evaluation codes from smooth quadric surfaces and twisted Segre varieties

2012
*
Designs, Codes and Cryptography
*

For hyperbolic

doi:10.1007/s10623-012-9692-4
fatcat:gdtltxakkbhjpd6xf3bxxxfrje
*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. ...##
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Intersection of two quadrics with no common hyperplane in P^n(F_q)
[article]

2009
*
arXiv
*
pre-print

Let Q_1 and Q_2 be two arbitrary

arXiv:0907.4556v1
fatcat:mlqgyfvwovfuxgci7h2xb4ipdi
*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*. ...##
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Notes on the Theory of Curves in the Affine Space

1930
*
Japanese Journal of Mathematics: Transactions and Abstracts
*

Journ., 31 (1929) In the following lines I will add

doi:10.4099/jjm1924.7.0_1
fatcat:tqepztyedvaencil7yrecte3ea
*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. ...##
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A remark on K3s of Todorov type (0,9) and (0,10)
[article]

2002
*
arXiv
*
pre-print

In other cases this is due to the structure of the Picard lattice and not only

arXiv:math/0205146v1
fatcat:cxbutovqczegnifjbgikumo5ua
*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. ...
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