In this note, we first establish a connection between the weight in the geometric invariant theory and the height introduced by Cornalba and Harris [CH] and Zhang [Z]. Then we give two applications. First, it provides a converse of Cornalba and Harris’s result, which can be treated as a function field analogue of Zhang’s theorem over number field. In particular, this connection gives a numerica...

Abstract We study the motivic and $$\ell $$ ℓ -adic realizations of dg category singularities zero locus a global section line bundle over regular scheme. will then use formula obtained in this way together with theorem due to D. Orlov J. Burke–M. Walker give for realization vector bundle. In particular, we obt...

We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X , with k > 1, then the Gauss map of order k has finite fibers, unless X = Pn is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a com...

Let H be an ample line bundle on a non-singular projective surface X , and M(H) the coarse moduli scheme of rank-two H-semistable sheaves with fixed Chern classes on X . We show that if H changes and passes through walls to get closer to KX , then M(H) undergoes natural flips with respect to canonical divisors. When X is minimal and κ(X) ≥ 1, this sequence of flips terminates in M(HX); HX is an...

Let X be a Kähler manifold of complex dimension n with smooth Kähler metric ω, and Z ⊂ X a smooth complex hypersurface. Let L→ X be a holomorphic line bundle with a possibly singular Hermitian metric e−φ whose singular locus does not lie in Z, i.e., such that e|Z is a metric for L|Z . Assume also that the line bundle EZ → X associated to the divisor Z has a holomorphic section fZ such that Z = ...

We prove that the kernel of evaluation morphism global sections - namely syzygy bundle a sufficiently ample line on an abelian variety is stable. This settles conjecture Ein-Lazarsfeld-Mustopa, in case varieties.

We prove the asymptotic of logarithmic Bergman kernel. And as an application, we calculate conditional expectation density zeros Gaussian random sections powers a positive line bundle that vanish along fixed smooth subvariety.

Natural convection heat transfer from a tube bundle in the indirect water bath heaters is investigated. A computer-code is used for the solution of the governing equations of mass, momentum and energy transfer based on the SIMPLE-C algorithm. Simulations are carried out for the gas pressure station heater of Kermanshah city with various tube bundle arrangements. In order to validate the numeric...