Search results
Results from the WOW.Com Content Network
In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry , it is a more general construction mapping a manifold to its Jacobi torus.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
Regular map may refer to: a regular map (algebraic geometry), in algebraic geometry, an everywhere-defined, polynomial function of algebraic varieties; a regular map (graph theory), a symmetric 2-cell embedding of a graph into a closed surface
In the particular case that Y equals A 1 the regular maps f : X→A 1 are called regular functions, and are algebraic analogs of smooth functions studied in differential geometry. The ring of regular functions (that is the coordinate ring or more abstractly the ring of global sections of the structure sheaf) is a fundamental object in affine ...
The period map is the map : ... Hodge Theory and Complex Algebraic Geometry I, II; Applications. Shimura curves within the locus of hyperelliptic Jacobians in genus ...
Maps of certain kinds have been given specific names. These include homomorphisms in algebra, isometries in geometry, operators in analysis and representations in group theory. [2] In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. A partial map is a partial function.
Contemporary algebraic geometry treats blowing up as an intrinsic operation on an algebraic variety. From this perspective, a blowup is the universal (in the sense of category theory ) way to turn a subvariety into a Cartier divisor .
In algebraic geometry and algebraic topology, branches of mathematics, A 1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to Fabien Morel and Vladimir Voevodsky.