the weighted projective space is called well-formed. The only singularities of weighted projective space are cyclic quotient singularities. A weighted projective...

f_{k})_{\bullet }}}} giving an embedding of projective varieties into projective schemes. Weighted projective spaces can be constructed using a polynomial ring...

In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in...

point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be...

examples come up when taking the stack quotient for weighted projective space/varieties. For example, the space P ( 2 , 3 ) {\displaystyle \mathbb {P} (2,3)}...

corresponds to the locus i ≠ j {\displaystyle i\neq j} . Using a weighted projective space and the Riemann–Hurwitz formula, a hyperelliptic curve can be...

varieties/orbifolds can be found as weighted complete intersections in a weighted projective space. The main tool for finding such spaces is the adjunction formula...

an intersection of spaces: Let Y 1 , Y 2 ⊂ X {\displaystyle Y_{1},Y_{2}\subset X} be projective subvarieties of a smooth projective variety. Then, we can...

\ldots ,g^{a_{n}}x_{n})} and the quotient of this action gives the weighted projective space W P ( a 0 , … , a n ) {\displaystyle \mathbb {WP} (a_{0},\ldots...

of a space X {\displaystyle X} into a space with known cohomology, such as P n {\displaystyle \mathbb {P} ^{n}} , or some weighted projective space. In...

the total space of E, often written just as E, and the projective cone Proj X ⁡ R {\displaystyle \operatorname {Proj} _{X}R} is the projective bundle of...

hypersurfaces in n-dimensional projective space is Fano if and only if the sum of their degrees is at most n. Weighted projective space P(a0,...,an) is a singular...

simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3-space P 3 {\displaystyle...

several databases of K3 surfaces with du Val singularities in weighted projective spaces. The Picard group Pic(X) of a complex analytic K3 surface X is...

fiber of a weighted homogenous polynomial, and also a formula for complements of weighted homogeneous polynomials in a weighted projective space.) Arapura...

{\mathcal {O}}(k)} over P n {\displaystyle \mathbb {P} ^{n}} is the weighted projective space minus a point O ( k ) = P ( 1 , … , 1 , k ) − { [ 0 : ⋯ : 0 :...

group is a subgroup of the projective group. For instance, Möbius transformations (transformations of the complex projective line, or Riemann sphere) are...

&0&1\end{array}}\right]} , the matrix becomes a projective transformation matrix (as it can also be used to perform projective transformations). This representation...

Space Cowboys is a 2000 American adventure drama film directed and produced by Clint Eastwood. It stars Eastwood, Tommy Lee Jones, Donald Sutherland,...

generalization of Salberger's global determinant method to the setting of weighted projective space. E. Bombieri, J. Pila, The number of integral points on arcs and...

2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick. The screenplay was written by Kubrick and Arthur C...

\mathrm {d} \mu (x)\right)^{1/p}} As L p {\displaystyle L^{p}} -spaces, the weighted spaces have nothing special, since L p ( S , w d μ ) {\displaystyle...

interpreted as a form of the plane sweep, in the projective dual of the input plane: a form of projective duality transforms the slope of a line in one plane...

projectivization of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system; for...

visualize perivascular spaces is T2-weighted MRI. The MR images of other neurological disorders can be similar to those of the dilated spaces. These disorders...

Space Jam is a 1996 American live-action animated sports comedy film directed by Joe Pytka and written by Leo Benvenuti, Steve Rudnick, Timothy Harris...

Office Space is a 1999 American satirical black comedy film written and directed by Mike Judge. It satirizes the office work life of a typical 1990s software...

Projective dual also maps planes to points, but it is not the case that both are reflections; instead, the projective dual switches between the space...

of orbifolds. Another commonly studied family of orbifolds are weighted projective spaces P ( n 1 , … , n k ) {\displaystyle \mathbb {P} (n_{1},\ldots ...

LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity)...