There is an action of $\mathbb{G}_m$ on $\mathbb{A}^3\setminus\{0\}$, and the
2 We prove that the tangent and the reflexivized cotangent sheaves of any normal projective klt Calabi-Yau or irreducible holomorphic symplectic variety are not pseudoeffective, generalizing results of A
5
The tangent sheaf and the sheaf of i-forms will be denoted by Θ X and Ωi X respectively
We only need to define the sheaf of differential operators D X and D X-modules will be sheaves on the Zariski site of X with a left module structure A tangent field to the mapping / is a pair (м, 0), where и is a holomorphic tangent field on X which projects under the mapping / to the tangent field в on S
The tangent sheaf referred to in the title is the sheaf of derivations T X / S = Hom O X (Ω X / S, O X) of a noetherian scheme X / S, where Ω X / S is the sheaf of relative differentials
LetA be anadmissibleHermitian–Yang–Mills(HYM)connectiononE withrespectto the Kähler metric ω
Foliations induced by Group Actions 14 References 22 1
Consider the holomorphic right action of G on the holomorphic tangent bundle \(TE_G\) induced by the right the Lie bracket operation of locally defined holomorphic vector fields on Z makes the coherent analytic sheaf TZ a sheaf of a holomorphic principal G-bundle admits a logarithmic connection singular over D if and
Then the orbifold tangent sheaf TS(−log()) is slope semistable with respect to L
This sheaf is the first syzygy of the Jacobian ideal sheaf JD of D, as the partial derivatives ∇(F) of F, that is, the generators of the Jacobian ideal JD, express it as the kernel of the Jacobian matrix of F: (1) 0 → TD → (N+1)
The question is then how to describe this subspace
$\begingroup$ It actually seems pretty intuitive to me that the tangent space of the ambient scheme at a point should be the same as the normal bundle of the point in the scheme --- intuitively the normal bundle measures how you can wiggle the point (subscheme), which is the same as the tangent space at that point
Similarly, if is a smooth function on an open set in , then the same formula defines a smooth function on the open set in ()