scholarly journals Toric complete intersections and weighted projective space

2003 ◽  
Vol 46 (2) ◽  
pp. 159-173 ◽  
Author(s):  
Maximilian Kreuzer ◽  
Erwin Riegler ◽  
David A. Sahakyan
Keyword(s):  
Projective Space ◽  
Weighted Projective Space ◽  
Complete Intersections

scholarly journals MIRROR MAPS AND INSTANTON SUMS FOR COMPLETE INTERSECTIONS IN WEIGHTED PROJECTIVE SPACE

1994 ◽  
Vol 09 (20) ◽  
pp. 1807-1817 ◽  
Author(s):  
ALBRECHT KLEMM ◽  
STEFAN THEISEN
Keyword(s):  
Projective Space ◽  
Complete Intersection ◽  
Weighted Projective Space ◽  
Complete Intersections

We consider a class of Calabi-Yau compactifications which are constructed as a complete intersection in weighted projective space. For manifolds with one Kähler modulus we construct the mirror manifolds and calculate the instanton sum.

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

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

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 Hyperbolicity related problems for complete intersection varieties

2013 ◽  
Vol 150 (3) ◽  
pp. 369-395 ◽  
Author(s):  
Damian Brotbek
Keyword(s):  
Projective Space ◽  
Existence Theorem ◽  
Complete Intersection ◽  
Cotangent Bundle ◽  
Projective Variety ◽  
Complete Intersections ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Complex Projective ◽  
Intersection Surface

AbstractIn this paper we examine different problems regarding complete intersection varieties of high multidegree in a smooth complex projective variety. First we prove an existence theorem for jet differential equations that generalizes a theorem of Diverio. Then we show how one can deduce hyperbolicity for generic complete intersections of high multidegree and high codimension from the known results on hypersurfaces. Finally, motivated by a conjecture of Debarre, we focus on the positivity of the cotangent bundle of complete intersections, and prove some results towards this conjecture; among other things, we prove that a generic complete intersection surface of high multidegree in a projective space of dimension at least four has an ample cotangent bundle.

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.

scholarly journals COMPLETE INTERSECTIONS AND MOVABLE CURVES ON THE MODULI SPACE OF SIX-POINTED RATIONAL CURVES

2012 ◽  
Vol 22 (06) ◽  
pp. 1250049
Author(s):  
PAUL L. LARSEN
Keyword(s):  
Projective Space ◽  
Complete Intersection ◽  
Moduli Space ◽  
Complex Projective Space ◽  
Projective Variety ◽  
Rational Curves ◽  
Complete Intersections ◽  
Family Of Curves ◽  
Complex Projective

A curve on a projective variety is called movable if it belongs to an algebraic family of curves covering the variety. We consider when the cone of movable curves can be characterized without existence statements of covering families by studying the complete intersection cone on a family of blow-ups of complex projective space, including the moduli space of stable six-pointed rational curves and the permutohedral or Losev–Manin moduli space of four-pointed rational curves. Our main result is that the movable and complete intersection cones coincide for the toric members of this family, but differ for the non-toric member, the moduli space of six-pointed rational curves. The proof is via an algorithm that applies in greater generality. We also give an example of a projective toric threefold for which these two cones differ.

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