From a May 2016 conference in Chicago, 15 papers explore local and global methods in algebraic geometry from such perspectives as the canonical map of some surfaces isogenous to a product, the degeneration of differentials and moduli of nodal curves on K3 surfaces, algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun, full cones swept out by minimal rational curves on irreducible Hermitian symmetric spaces as examples of varieties underlying geometric substructures, and Skoda's ideal generation from vanishing theorem for semipositive Nakano curvature and

Cauchy-Schwarz inequality for tensors.

From this equation, using the

Cauchy-Schwarz inequality, we obtain that [parallel][[??].sup.n][parallel] [less than or equal to] [parallel][p.sup.n-1][parallel].

By the Hardy inequality [mathematical expression not reproducible] and by the

Cauchy-Schwarz inequality, changing [xi] = [eta]y we find

We say that a geodesic metric space (X, d) satisfies the

Cauchy-Schwarz inequality if

Integrating (20) over (0, t), using

Cauchy-Schwarz inequality and (18), we obtain for any [p.sub.1] > 0

Using [epsilon]-inequality and

Cauchy-Schwarz inequality we obtain

Recalling the

Cauchy-Schwarz inequality, we obtain the formula below:

Then, applying

Cauchy-Schwarz inequality and (33), we obtain for any v [member of] W

By the

Cauchy-Schwarz inequality and changing the order of integration, we have

From

Cauchy-Schwarz inequality [absolute value of <[a.sub.i], [a.sub.j]>] [less than or equal to] [[parallel] [a.sub.i][parallel].sub.2] [[parallel][a.sub.J][parallel].sub.2], it is clear that the mutual coherence of any matrix A is bounded by 1.

In the 3D space [R.sup.(3)] for any couple vectors the

Cauchy-Schwarz inequality is true that for the vectors (1) inequality gives an implication

Using the triangle inequality and

Cauchy-Schwarz inequality, we have