Family 033Algebraic and complex geometryNo LeanNot yet digested

Iitaka subadditivity, variation, and logarithmic additivity

Proves Campana's orbifold Iitaka subadditivity conjecture for smooth Fujiki-class-

\mathcal C

manifolds with rational simple-normal-crossing boundaries. For projective fibrations

f:U\to V

of smooth complex quasi-projective varieties with connected fibers, general fiber F, and

\bar\kappa(V)\ge0

, proves Popa's inequality

\bar\kappa(U)\ge\kappa(F)+\max\{\bar\kappa(V),\mathop{\mathrm{Var}}\nolimits (f)\}

, where variation measures the whole geometric generic fiber.

Manuscripts in this family · 5

Orbifold and logarithmic Iitaka subadditivity

Sep 26, 2026·paper.pdf

We prove Campana's orbifold Iitaka subadditivity conjecture for rational simple normal crossing boundaries on compact manifolds in Fujiki class

\mathcal C

, including coefficient one. Ordinary and logarithmic subadditivity follow.

Full abstract

PDF on GitHub LaTeX source

Logarithmic Kodaira dimension and whole-fiber variation

Sep 26, 2026·paper.pdf

We prove the logarithmic Iitaka–Viehweg inequality for projective surjective morphisms with connected fibers between smooth complex quasi-projective varieties whose base has nonnegative logarithmic Kodaira dimension. The variation measures the birational field of definition of the whole geometric generic fiber. This resolves Popa's logarithmic variation conjecture positively.

Full abstract

PDF on GitHub LaTeX source

The reverse logarithmic Kodaira inequality and additivity

Sep 26, 2026·paper.pdf

We prove the reverse logarithmic Kodaira inequality for a surjective connected-fiber morphism

f:(X,E)\to(Y,D)

of smooth projective reduced simple-normal-crossing pairs, with

\mathop{\mathrm{Supp}}\nolimits (f^*D)\subseteq\mathop{\mathrm{Supp}}\nolimits E

, such that X and every boundary stratum are smooth over

Y\setminus\mathop{\mathrm{Supp}}\nolimits D

. Together with logarithmic subadditivity, the inequality gives additivity, including both negative-infinity cases. This resolves Popa's logarithmic additivity conjecture positively in the projective reduced-SNC, stratum-smooth setting.

Full abstract

PDF on GitHub LaTeX source

Projective Hodge lines and ordinary Iitaka subadditivity

Sep 27, 2026·paper.pdf

We prove the ordinary Iitaka subadditivity conjecture for surjective projective morphisms with connected fibers between smooth connected projective varieties over algebraically closed fields of characteristic zero. If F is the geometric generic fiber of

f:X\to Z

, then

\kappa(X)\geq\kappa(F)+\kappa(Z)

Full abstract

PDF on GitHub LaTeX source

B-semiampleness for compact log-smooth Kähler fibrations

Sep 10, 2026·paper.pdf

We prove the compact log-smooth Kähler case of b-semiampleness. Let

f:Y\to X

be a surjective holomorphic map with connected fibers between smooth compact connected Kähler manifolds, and let Δ be an effective rational divisor with simple normal crossing support and coefficients in

[0,1]

, with

K_Y+\Delta\sim_{\mathbb Q}f^*L

for

L\in\mathop{\mathrm{Pic}}\nolimits (X)_{\mathbb Q}

. There is a smooth compact Kähler modification

S\to X

for which the threshold-moduli line satisfies

M_{S_1}=\nu^*M_S

\mathop{\mathrm{Pic}}\nolimits (S_1)_{\mathbb Q}

for every smooth compact Kähler modification

\nu:S_1\to S

, and some positive multiple of M

_{S}

is represented by a holomorphic line bundle generated by global sections. Horizontal components of coefficient one are allowed; neither projectivity nor a Campana orbifold Iitaka hypothesis is assumed.

Full abstract

PDF on GitHub LaTeX source