Twisted jets, motivic measures and orbifold cohomology

Yasuda, Takehiko

doi:10.1112/s0010437x03000368

Cited by 71 publications

(81 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, the same holds true for complex tori. Another theorem, originally due to Batyrev and Kontsevich, says that two birational Calabi-Yau manifolds have the same Betti numbers and Hodge numbers [1,4,10,19,21]. However, there are rigid birational non-isomorphic Calabi-Yau manifolds (cf.…”

Section: Introductionmentioning

confidence: 99%

Connecting certain rigid birational non-homeomorphic Calabi-Yau threefolds via Hilbert scheme

Lee

Oguiso

2009

Communications in Analysis and Geometry

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Connecting certain rigid birational non-homeomorphic Calabi-Yau threefolds via Hilbert scheme

Lee

Oguiso

2009

Communications in Analysis and Geometry

View full text Add to dashboard Cite

show abstract

“…These results have been extended to general (not necessarily global quotient) orbifolds independently by Yasuda [43] and by Lupercio-Poddar [27].…”

Section: Simple Normal Crossing Resolution Of the Pair (Y D)mentioning

confidence: 84%

A localization principle for orbifold theories

Uribe¹,

Fernex²,

Nevins³

et al. 2006

Recent Developments in Algebraic Topology

View full text Add to dashboard Cite

Abstract. In this article, written primarily for physicists and geometers, we survey several manifestations of a general localization principle for orbifold theories such as K-theory, index theory, motivic integration and elliptic genera. OrbifoldsIn this paper we will attempt to explain a general localization principle that appears frequently under several guises in the study of orbifolds. We will begin by reminding the reader what we mean by an orbifold.The most familiar situation in physics is that of an orbifold of the type X = [M/G], where M is a smooth manifold and G is a finite group acting 1 smoothly on M ; namely, we give ourselves a homomorphism G → Diff(M ). We make a point of distinguishing the orbifold X = [M/G] from its quotient space (also called orbit space) X = M/G. As a set, as we know, a point in X is an orbit of the action: that is, a typical element of M/G is Orb(x) = {xg | g ∈ G}.For us an orbifold X = [M/G] is a smooth category 2 (actually a topological groupoid) whose objects are the points of M , X 0 = Obj(X) = M , and we insist on remembering that X 0 = Obj(X) is a smooth manifold. The arrows of this category are X 1 = Mor(X) = M × G again thinking of it as a smooth manifold. A typical arrow in this category is

show abstract

“…By a result of Yasuda [9] this does not depend on the choice of Y . The dimensions of the stringy cohomology spaces H k str (X; R) are given by Batyrev's stringy Betti numbers [2].…”

Section: Introductionmentioning

confidence: 89%