Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sławomir Cynk
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Weighted Projective Space ◽  
Hodge Numbers ◽  
Triple Points

Abstract We give a formula for the Hodge numbers of a three-dimensional hypersurface in a weighted projective space with only ordinary triple points as singularities.

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

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

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 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.

scholarly journals Circle of Sarkisov Links on a Fano 3-Fold

2016 ◽  
Vol 60 (1) ◽  
pp. 1-16
Author(s):  
Hamid Ahmadinezhad ◽  
Francesco Zucconi
Keyword(s):  
Projective Space ◽  
Weighted Projective Space ◽  
Birational Maps

AbstractFor a general Fano 3-fold of index 1 in the weighted projective space ℙ(1, 1, 1, 1, 2, 2, 3) we construct two new birational models that are Mori fibre spaces in the framework of the so-called Sarkisov program. We highlight a relation between the corresponding birational maps, as a circle of Sarkisov links, visualizing the notion of relations in the Sarkisov program.

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