相关论文: On the termination of flips for log canonical gene…

It is proved that the global log canonical threshold of a Zariski general Fano complete intersection of index 1 and codimension $k$ in ${\mathbb P}^{M+k}$ is equal to one, if $M\geqslant 2k+3$ and the maximum of the degrees of defining…

In this paper, we study the geometry of trisections on certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in order to construct trisections and related plane curves with interesting properties…

Recently, by studying an explicit basis, K\"ock and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof…

We prove that the canonical ring of a smooth projective variety is finitely generated.

We prove boundedness of global strong $(\delta,n)$-complements for generalized $\epsilon$-log canonical pairs of Fano type. We also prove some partial results towards boundedness of local strong $(\delta,n)$-complements for semi-stable…

We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened $K_{3,m}$'s. Our construction is explicit,…

This paper aims to study the decomposition group of a nonsingular plane cubic under the light of the log Calabi-Yau geometry. Using this approach we prove that an appropriate algorithm of the Sarkisov Program in dimension 2 applied to an…

The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of…

Several results in recent years have shown that the usual generalizations of taut foliations to higher dimensions, based only on topological concepts, lead to a theory that lacks the complexity of its 3-dimensional counterpart. Instead, we…

The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.

Termination of logic programs with negated body atoms (here called general logic programs) is an important topic. One reason is that many computational mechanisms used to process negated atoms, like Clark's negation as failure and Chan's…

Starting from Wilson's action, we calculate strong coupling series for the Polyakov loop susceptibility in lattice gauge theories for various small N_\tau in the thermodynamic limit. Analysing the series with Pad\'e approximants, we…

We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal…

The normalization of a quasi-log canonical pair is a quasi-log canonical pair.

We construct a Zariski decomposition for cycle classes of arbitrary codimension. This decomposition is an analogue of well-known constructions for divisors. Examples illustrate how Zariski decompositions of cycle classes reflect the…

We show some inductive statements for the index conjecture for log canonical Calabi-Yau pairs. Using it, we show that boundedness of log canonical index for log canonical Calabi Yau pairs with rational DCC coefficients in dimension 3. We…

We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…

We apply the specialization technique based on the decomposition of the diagonal to find an explicit example over $\mathbb{Q}$ of a quadric and cubic hypersurface in $\mathbb{P}^6$ such that their intersection is a smooth stably irrational…

We prove that the target space of an extremal Fano contraction from a log canonical pair has only log canonical singularities. We also treat some related topics, for example, the finite generation of canonical rings for compact K\"ahler…

Minimal log discrepancies (mld's) are related not only to termination of log flips, and thus to the existence of log flips but also to the ascending chain condition (acc) of some global invariants and invariants of singularities in the Log…