Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic $$p>0$$ and log weak Lefschetz conjecture for log crystalline cohomologies

Non-vanishing Theorem for Log Canonical Pairs

We obtain a correct generalization of Shokurov’s nonvanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary, we obtain the cone theorem for log canonical pairs. We do not need Ambro’s theory of quasi-log varieties.

StUSPACE(log n) <= DSPACE(log²n / log log n)

We present a deterministic algorithm running in space O ? log 2 n= log logn solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) time-bounded algorithm for this problem running on a parallel pointer machine.

Canon-log Transfer Characteristic

On Kodaira Energy of Polarized Log Varieties

In this paper we are mainly interested in the case κǫ < 0, or equivalently, K(V,B) is not pseudo-effective. According to the classification philosophy, at least when B = 0, V should admit a Fano fibration structure in such cases. In §2, by using Log Minimal Model Program which is available in dimension ≤ 3 at present (cf. [Sho], [Ko]), we establish the existence of such a fibration in the polar...

An Application of a Log Version of the Kodaira Vanishing Theorem to Embedded Projective Varieties

The idea in this paper is to show how a generalized “log” version of the Kodaira vanishing theorem can be employed to improve the results of Theorem 1 (which was also proved by Kodaira vanishing) when we have more knowledge about the equations for Y . The idea is to find a hypersurface F ⊂ P which has high multiplicity along Y , is “log canonical” near Y , and has relatively small degree, then ...