scholarly journals THE COHOMOLOGICAL CREPANT RESOLUTION CONJECTURE FOR ℙ(1,3,4,4)

2009 ◽  
Vol 20 (06) ◽  
pp. 791-801 ◽  
Author(s):  
S. BOISSIÈRE ◽  
E. MANN ◽  
F. PERRONI
Keyword(s):  
Projective Space ◽  
Cohomology Ring ◽  
Weighted Projective Space ◽  
Crepant Resolution ◽  
Crepant Resolution Conjecture

We prove the cohomological crepant resolution conjecture of Ruan for the weighted projective space ℙ(1,3,4,4). To compute the quantum corrected cohomology ring, we combine the results of Coates–Corti–Iritani–Tseng on ℙ(1,1,1,3) and our previous results.

scholarly journals Computing certain Gromov-Witten invariants of the crepant resolution of ℙ(1, 3, 4, 4)

2011 ◽  
Vol 201 ◽  
pp. 1-22
Author(s):  
Samuel Boissière ◽  
Étienne Mann ◽  
Fabio Perroni
Keyword(s):  
Projective Space ◽  
Weighted Projective Space ◽  
Crepant Resolution ◽  
Genus Zero ◽  
Marked Points ◽  
Formula Computing

AbstractWe prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversalA3-singularity of the weighted projective space ℙ(1,3,4,4) using the theory of deformations of surfaces withAn-singularities. We use this result to check Ruan’s conjecture for the stack ℙ(1,3,4,4).

scholarly journals The equivariant cohomology ring of weighted projective space

2009 ◽  
Vol 146 (2) ◽  
pp. 395-405 ◽  
Author(s):  
ANTHONY BAHRI ◽  
MATTHIAS FRANZ ◽  
NIGEL RAY
Keyword(s):  
Projective Space ◽  
Chern Class ◽  
Equivariant Cohomology ◽  
Cohomology Ring ◽  
Weighted Projective Space ◽  
Generators And Relations ◽  
Piecewise Polynomials ◽  
Projective Bundles

AbstractWe describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula for weighted projective bundles.

scholarly journals CHEN–RUAN COHOMOLOGY OF ADE SINGULARITIES

2007 ◽  
Vol 18 (09) ◽  
pp. 1009-1059 ◽  
Author(s):  
FABIO PERRONI
Keyword(s):  
Cohomology Ring ◽  
Crepant Resolution ◽  
The Family ◽  
Crepant Resolution Conjecture

We study Ruan's cohomological crepant resolution conjecture [41] for orbifolds with transversal ADE singularities. In the An-case, we compute both the Chen–Ruan cohomology ring [Formula: see text] and the quantum corrected cohomology ring H*(Z)(q1,…,qn). The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between [Formula: see text] and H*(Z)(-1) in the A1-case, verifying Ruan's conjecture. In the An-case, the family H*(Z)(q1,…,qn) is not defined for q1 = ⋯ = qn = -1. This implies that the conjecture should be slightly modified. We propose a new conjecture in the An-case (Conjecture 1.9). Finally, we prove Conjecture 1.9 in the A2-case by constructing an explicit isomorphism.

scholarly journals Computing certain Gromov-Witten invariants of the crepant resolution of ℙ(1, 3, 4, 4)

2011 ◽  
Vol 201 ◽  
pp. 1-22 ◽  
Author(s):  
Samuel Boissière ◽  
Étienne Mann ◽  
Fabio Perroni
Keyword(s):  
Projective Space ◽  
Weighted Projective Space ◽  
Crepant Resolution ◽  
Genus Zero ◽  
Marked Points ◽  
Formula Computing

AbstractWe prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal A3-singularity of the weighted projective space ℙ(1,3,4,4) using the theory of deformations of surfaces with An-singularities. We use this result to check Ruan’s conjecture for the stack ℙ(1,3,4,4).

scholarly journals The Chen–Ruan Cohomology of Weighted Projective Spaces

2007 ◽  
Vol 59 (5) ◽  
pp. 981-1007 ◽  
Author(s):  
Yunfeng Jiang
Keyword(s):  
Projective Space ◽  
Cohomology Ring ◽  
Projective Spaces ◽  
Weighted Projective Space ◽  
Line Bundles ◽  
Cup Product ◽  
Direct Sum

AbstractIn this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space

scholarly journals Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Andrew J. McLeod ◽  
Cristian Vergu ◽  
Matthias Volk ◽  
Matt von Hippel ◽  
...  
Keyword(s):  
Projective Space ◽  
Feynman Integral ◽  
Weighted Projective Space

scholarly journals On the arithmetic of a family of degree - two K3 surfaces

2018 ◽  
Vol 166 (3) ◽  
pp. 523-542 ◽  
Author(s):  
FLORIAN BOUYER ◽  
EDGAR COSTA ◽  
DINO FESTI ◽  
CHRISTOPHER NICHOLLS ◽  
MCKENZIE WEST
Keyword(s):  
Projective Space ◽  
Function Field ◽  
Weighted Projective Space ◽  
Module Structure ◽  
K3 Surface ◽  
Galois Module ◽  
Generic Element ◽  
The Family ◽  
Formula Group ◽  
Image Position

AbstractLet ℙ denote the weighted projective space with weights (1, 1, 1, 3) over the rationals, with coordinates x, y, z and w; let $\mathcal{X}$ be the generic element of the family of surfaces in ℙ given by \begin{equation*} X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \end{equation*} The surface $\mathcal{X}$ is a K3 surface over the function field ℚ(t). In this paper, we explicitly compute the geometric Picard lattice of $\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\mathcal{X}$ and other elements of the family X.

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