Related papers: Note on quasi-numerically positive log canonical d…
We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.
We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.
Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria…
We show that the crossing number of any link that is known to be quasi-alternating is less than or equal to its determinant. Based on this, we conjecture that the crossing number of any quasi-alternating link is less than or equal to its…
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.
A simple and general prescription for evaluating unambiguously the sign of the grand-canonical trace of quasi-particle statistical density operators (the so-called sign ambiguity in taking the square root of determinants) is given. Sign…
We show that the number of positive integers $n\leq N$ such that $\mathbb{Z}/(n^2+n+1)\mathbb{Z}$ contains a perfect difference set is asymptotically $N/\log{N}$.
In this paper, we use canonical bundle formulas to prove some generalizations of an old theorem of Kawamata on the semiampleness of nef and abundant log canonical divisors. In particular, we show that for klt pairs $(X,B)$ with $K_X+B$…
We introduce and study a log discrepancy function on the space of semivaluations centered on an integral noetherian scheme of positive characteristic. Our definition shares many properties with the analogue in characteristic zero; we prove…
In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.
We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…
In terms of log canonical threshold, we characterize plurisubharmonic functions with logarithmic asymptotical behaviour.
We prove Koll\'ar-type effective basepoint-free theorems for quasi-log canonical pairs.
We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
This is a short note on the log canonical inversion of adjunction.
The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…
We give a sufficient condition for the termination of flips. Then we discuss a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor as an application. We also treat a slight refinement of dlt…
We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
We study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the…
A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the…