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{Hilb} (n,P)} is non-empty, and Robin Hartshorne (1966) showed that if H i l b ( n , P ) {\displaystyle \mathbf {Hilb} (n,P)} is non-empty then it is linearly...

(possibly empty). These definitions are from (Mumford 1977) and are not equivalent to the ones in the first edition of Mumford's book. Many moduli spaces...

In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed...

In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes...

partially ordered set are sets of vertices with either zero vertex (the empty set), one vertex, two vertices (an edge), or the entire vertex set (a two-dimensional...

\Omega G_{2})} . If G 2 {\displaystyle G_{2}} is empty, then the quotient space is an orbifold. If G 2 {\displaystyle G_{2}} is not empty, then it is an...

one of the manifolds can be empty; in particular a closed manifold of dimension n+1 is viewed as an endomorphism of the empty set. One can also compose...

{\mathcal {X}}} of groupoids over S {\displaystyle S} that is locally non-empty (each point p ∈ S {\displaystyle p\in S} has an open neighbourhood U p {\displaystyle...

actual dimension away from the reducibles. It means that the moduli space is generically empty if the virtual dimension is negative. For a self dual 2 form...

the number zero is necessary in mathematics, so also every set has the empty set ∅ as a subset. In an abstract polytope ∅ is by convention identified...

let τ be a family of subsets of X. Then τ is called a topology on X if: Both the empty set and X are elements of τ. Any union of elements of τ is an element...

the moduli of curves of genus g {\displaystyle g} and is denoted as M g {\displaystyle {\mathfrak {M}}_{g}} . There are few ways to show this moduli has...

accounts for 26.8% of the cosmic contents. Dark energy, which is the energy of empty space and is causing the expansion of the universe to accelerate, accounts...

given the cocountable topology, in which a set is defined as open if it is either empty or its complement is countable. When the set is uncountable, this...

Picard number ρ ≥ 3 {\displaystyle \rho \geq 3} . If the set of roots Δ {\displaystyle \Delta } is empty, then the closed cone of curves is the closure of...

d-dimensional empty manifold and Z( ∅ {\displaystyle \emptyset } ) = 1 for the (d + 1)-dimensional empty manifold. Z(M*) = Z(M) (the hermitian axiom). If ∂ M =...

general relativity. If considered as a "source term" in the field equation, it can be viewed as equivalent to the mass of empty space (which conceptually...

\operatorname {H} ^{*}(\operatorname {Bun} _{G}(X),\mathbb {Q} _{l})} of the moduli stack of principal bundles is a free graded-commutative algebra on certain...

complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. Theta functions are parametrized...

in particular ⁠ G d r {\displaystyle G_{d}^{r}} ⁠ is empty if ρ < 0). David Gieseker proved that if C is generic then ⁠ G d r {\displaystyle G_{d}^{r}}...