Building on work of the fourth author and Morelli's work, we prove the weak factorization
conjecture for birational maps in characteristic zero: a birational map between complete …

This is an introduction to a very active field of research, on the boundary between
mathematics and physics. It is aimed at graduate students and researchers in geometry and …

Geometry on Arc Spaces of Algebraic Varieties Page 1 Geometry on Arc Spaces of Algebraic
Varieties Jan Denef and Fran<;ois Loeser Abstract. This paper is a survey on arc spaces, a …

An n-jet of an arc in an algebraic variety is a one parameter Taylor series of length n in that
variety. To be precise, if the variety X is defined over the algebraically closed field k, then it is …

We prove that if X is a locally complete intersection variety, then X has all the jet schemes
irreducible if and only if X has canonical singularities. After embedding X in a smooth variety …

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define
stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a …

ProQuest Dissertations Page 1 FJRW Rings and Landau-Ginzburg Mirror Symmetry by Marc
Krawitz A dissertation submitted in partial fulfillment of the requirements for the degree of …

La correspondance de McKay Page 1 Astérisque MILES REID La correspondance de
McKay Astérisque, tome 276 (2002), Séminaire Bourbaki, exp. no 867, p. 53-72 <http://www.numdam.org/item?id=SB_1999-2000__42__53_0> …

The study of singularities of pairs is fundamental for higher dimensional birational geometry.
The usual approach to invariants of such singularities is via divisorial valuations, as in [Kol] …

Let $ X $ be a smooth variety and $ Y\subset X $ a closed subscheme. We use motivic
integration on the space of arcs of $ X $ to characterize the fact that $(X, Y) $ is log canonical …