Related papers: On minimal model theory for algebraic log surfaces
We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical…
We classify all the effective anticanonical divisors on weak del Pezzo surfaces. Through this classification we obtain the smallest number among the log canonical thresholds of effective anticanonical divisors on a given Gorenstein…
In this paper we prove a desingularization theorem for Legendrian surfaces that are the conormal of a quasi-ordinary hypersurface.
In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function $P: \mathbb Z_{\geq 0}\to \mathbb Z $, then there exists an integer $N_1>0$ such that if…
We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…
We prove a formula of log canonical models for moduli space $\bar{M}_{g,n}$ of pointed stable curves which describes all Hassett's moduli spaces of weighted pointed stable curves in a single equation. This is a generalization of the…
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…
We study global log canonical thresholds of cubic surfaces with canonical singularities, and we prove the existence of a Kahler-Einstein metric on two singular cubic surfaces.
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
We establish the minimal model program (MMP) for generalized foliated threefolds $(X, \mathcal{F}, B, \mathbf{M})$ of rank 1, extending the result of Cascini and Spicer in [CS25d]. As an application of the generalized foliated MMP, we prove…
The LCS locus is an essential ingredient in the proof of fundamental results of Log Minimal Model Program, such as nonvanishing and base point freeness theorems. We prove in this paper that the LCS locus of a log canonical variety has…
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way…
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with…
We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…
We extend the assertion of the Generalized Lower Bound Theorem (GLBT) to general polytopes under the assumption that their low dimensional skeleton is simplicial, with partial results for the general case. We prove a quantitative version of…
A product-quotient surface is the minimal resolution of the singularities of the quotient of a product of two curves by the action of a finite group acting separately on the two factors. We classify all minimal product-quotient surfaces of…
We identify quotient polynomial rings isomorphic to the recently found fundamental fusion algebras of logarithmic minimal models.
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
In this paper, we employ the loop group method to study the construction of minimal Lagrangian surfaces in the complex projective plane for which the surface is contractible. We present several new classes of minimal Lagrangian surfaces in…
This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Bj\"{o}rling-Schwarz formula in the domain where it is valid, changing the normal…