Results 11 to 20 of about 461,075 (111)
Spin(7)-Manifolds and Multisymplectic Geometry [PDF]
, 2021 We utilize Spin(7) identities to prove that the Cayley four-form associated to a torsion-free Spin(7)-Structure is non-degenerate in the sense of multisymplectic geometry. Therefore, Spin(7) geometry may be treated as a special case of multisymplectic geometry.
arxiv +1 more source
Some remarks on multiplicity codes
, 2014 Multiplicity codes are algebraic error-correcting codes generalizing classical polynomial evaluation codes, and are based on evaluating polynomials and their derivatives.
Kopparty, Swastik
core +1 more source
Galois groups of Schubert problems via homotopy computation
, 2007 Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics.
Leykin, Anton, Sottile, Frank
core +8 more sources
A view on extending morphisms from ample divisors
, 2009 The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sections" was one of the classical principles of projective geometry.
Beltrametti, Mauro C., Ionescu, Paltin
core +2 more sources
On the Riemannian geometry of Seiberg-Witten moduli spaces [PDF]
, 2007 We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.
arxiv +1 more source
Pseudo-Riemannian geometry in terms of multi-linear brackets [PDF]
, 2013 We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)K\"ahler geometry.
arxiv +1 more source
Teaching mental mathematics from level 5 (National Strategies; Secondary) [PDF]
, 2005 An introduction to a set of materials describing teaching approaches that can be used to develop mental mathematics abilities beyond level 5, covering number, algebra, geometry and statistics.
core
Do the Angles of a Triangle Add up to 180°? -- Introducing Non-Euclidean Geometry [PDF]
arXiv, 2021 How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways of introducing non-Euclidean geometry to students and the general public using different physical models, including chalksphere, crocheted hyperbolic surfaces,
arxiv
Footnotes to the birational geometry of primitive symplectic varieties
, 2023 In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.Comment: Final version. To appear in "Perspectives on four decades. Algebraic Geometry 1980 - 2020.
Lehn, Christian +2 more
core
Hessian Geometry and Phase Change of Gibbons-Hawking Metrics [PDF]
arXiv, 2018 We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.
arxiv