인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.

/pdf/existence-of-minimal-models-for-varieties-of-log-general-43vm28b5my.pdf

Existence of minimal models for varieties of log general type

Let 
$X$
 be an algebraic stack in the sense of Deligne-Mumford. We construct a purely 
$0$
 -dimensional algebraic stack over 
$X$
 (in the sense of Artin), the intrinsic normal cone 
${\frak C}_X$
 . The notion of (perfect) obstruction theory for 
$X$
 is introduced, and it is shown how to construct, given a perfect obstruction theory for 
$X$
 , a pure-dimensional virtual fundamental class in the Chow group of 
$X$
 . We then prove some properties of such classes, both in the absolute and in the relative context. Via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory, and sometimes a perfect one.

The intrinsic normal cone

Parameter spaces: constructions and examples * Basic facts about moduli spaces of curves * Techniques * Construction of M_g * Limit Linear Series and the Brill-Noether Theory * Geometry of moduli spaces: Selected Results.

Moduli of curves

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed.

https://link.springer.com/content/pdf/10.1007/s002220050293.pdf

Localization of virtual classes

Intersection theory on algebraic stacks and on their moduli spaces.

Given a smooth complex Deligne-Mumford stack ${\cal X}$ with a projective coarse moduli space, we introduce Gromov-Witten invariants of ${\cal X}$ and prove some of their basic properties, including the WDVV equation.

Gromov-Witten theory of Deligne-Mumford stacks

We study the structure of the stacks of twisted stable maps to the classifying stack of a finite group G—which we call the stack of twisted G-covers, or twisted G-bundles. For a suitable group Gwe show that the substack corresponding to admissible G-covers is a smooth projective fine moduli space. Dedicated to Steven L. Kleiman on the occasion of his 60th birthday.

Twisted Bundles and Admissible Covers

Nous introduisons et etudions, en caracteristique positive et mixte, une classe de champs algebriques a champs d'inertie finis, appeles champs algebriques moderes. Cette classe inclue les champs moderes de Deligne-Mumford, et on peut dire qu'elle se comporte mieux que la classe des champs generaux de Deligne-Mumford. En outre, nous donnons une caracterisation complete des schemas en groupes finis plats et lineairement reductifs sur une base quelconque. Notre resultat principal est le suivant : un champ algebrique modere est, localement dans la topologie etale, un quotient par une action d'un schema en groupes fini lineairement reductif.

/pdf/tame-stacks-in-positive-characteristic-4rpldhntse.pdf

Tame stacks in positive characteristic

The cherry on top of this stacky paper is the following: for any g>1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space of stable curves. 
The proof relies on methods introduced by Looijenga and Pikaart-De Jong, and on the theory of twisted G-covers, a theory announced without proofs in math.AG/9811059, section 3, and developed in the first few sections of this paper. This includes a moduli description of the normalization of the Harris-Mumford space of admissible covers, and a study of moduli of stable curves with abelian and non-abelian level structure.

Angelo Vistoli

Papers

Intersection theory on algebraic stacks and on their moduli spaces.

Gromov-Witten theory of Deligne-Mumford stacks

Twisted Bundles and Admissible Covers

Tame stacks in positive characteristic

Twisted bundles and admissible covers