scholarly journals Algebraic Reduced Genus One Gromov–Witten Invariants for Complete Intersections in Projective Spaces

2019 ◽  
Author(s):  
Sanghyeon Lee ◽  
Jeongseok Oh
Keyword(s):  
Algebraic Geometry ◽  
Vector Bundle ◽  
Complete Intersection ◽  
Comparison Theorem ◽  
Euler Number ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Dimension 2 ◽  
Definition Of ◽  
Genus One

Abstract In [ 17, 18], Zinger defined reduced Gromov–Witten (GW) invariants and proved a comparison theorem of standard and reduced genus one GW invariants for every symplectic manifold (with all dimension). In [ 3], Chang and Li provided a proof of the comparison theorem for quintic Calabi–Yau three-folds in algebraic geometry by taking a definition of reduced invariants as an Euler number of certain vector bundle. In [ 5], Coates and Manolache have defined reduced GW invariants in algebraic geometry following the idea by Vakil and Zinger in [ 14] and proved the comparison theorem for every Calabi–Yau threefold. In this paper, we prove the comparison theorem for every (not necessarily Calabi–Yau) complete intersection of Dimension 2 or 3 in projective spaces by taking a definition of reduced GW invariants in [ 5].

scholarly journals Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Svetlana Ermakova
Keyword(s):  
Vector Bundle ◽  
Complete Intersection ◽  
Finite Rank ◽  
Vector Bundles ◽  
Complete Intersections ◽  
Finite Codimension ◽  
Line Bundles ◽  
Direct Sum ◽  
Rank Vector

AbstractIn this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.

(0,2) CALABI–YAU SIGMA MODELS AND THEIR DUALITY

1998 ◽  
Vol 13 (05) ◽  
pp. 779-796
Author(s):  
MAKOTO SAKAGUCHI
Keyword(s):  
Vector Bundle ◽  
Sigma Models ◽  
Complete Intersection ◽  
Heterotic String ◽  
Dual Pairs ◽  
Direct Sum ◽  
Phase Structures ◽  
Heterotic String Theories ◽  
Linear Sigma Models ◽  
Definition Of

N=(0,2) heterotic string theories on Calabi–Yau spaces are considered based on linear sigma approaches. We construct (0,2) sigma models on complete intersection Calabi–Yau spaces, ℳ, realized in a product of weighted projective spaces. The definition of the associating vector bundle V over ℳ is given. These models are formulated as the IR limits of (0,2) U (1)N gauged linear sigma models. Examining their phase structures, we observe that there are hybrid phases where one cannot intrinsically distinguish between the defining polynomials of the Calabi–Yau space ℳ and those of the gauge bundle V. Thus we construct dual pairs of two (0,2) Calabi–Yau sigma models which are isomorphic in their hybrid phases. In addition, generalizing the gauge bundle into the direct sum of bundles, we study the duality of (0,2) string vacua.

scholarly journals ELLIPTIC GENERA OF COMPLETE INTERSECTIONS

2005 ◽  
Vol 16 (10) ◽  
pp. 1131-1155 ◽  
Author(s):  
XIAOGUANG MA ◽  
JIAN ZHOU
Keyword(s):  
Projective Spaces ◽  
Complete Intersections ◽  
Elliptic Genera ◽  
Elementary Argument ◽  
Definition Of

We propose a new definition of the elliptic genera for complete intersections, not necessarily nonsingular, in projective spaces. We also prove they coincide with the expressions obtained from Landau–Ginzburg model by an elementary argument.

scholarly journals GV-spectroscopy for F-theory on genus-one fibrations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Paul-Konstantin Oehlmann ◽  
Thorsten Schimannek
Keyword(s):  
Complete Intersection ◽  
Complete Intersections ◽  
Detailed Knowledge ◽  
Gauge Groups ◽  
Frobenius Method ◽  
Codimension Two ◽  
Novel Technique ◽  
Genus One

Abstract We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau d-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary polytope. In particular for fibers that generically lead to multiple sections, only multi-sections or that are complete intersections in higher codimension, our technique is vastly more efficient than classical approaches. As an application we study two Higgs chains of six-dimensional supergravities that are engineered by fibrations of codimension two complete intersection fibers. Both chains end on a vacuum with G = ℤ4 that is engineered by fibrations of bi-quadrics in ℙ3. We use the detailed knowledge of the structure of the reducible fibers that we obtain from GV-spectroscopy to comment on the corresponding Tate-Shafarevich group. We also show that for all fibers the six-dimensional supergravity anomalies including the discrete anomalies generically cancel.

scholarly journals Quadro-quadric special birational transformations from projective spaces to smooth complete intersections

2016 ◽  
Vol 27 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Qifeng Li
Keyword(s):  
Complete Intersection ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Fano Manifold ◽  
Birational Transformations ◽  
Base Locus ◽  
Birational Transformation

Let [Formula: see text] a birational transformation with a smooth connected base locus scheme, where [Formula: see text] is a nondegenerate prime Fano manifold covered by lines. We call [Formula: see text] a quadro-quadric special briational transformation if [Formula: see text] and [Formula: see text] are defined by linear subsystems of [Formula: see text] and [Formula: see text] respectively. In this paper, we classify quadro-quadric special birational transformations in the cases where either (i) [Formula: see text] is a complete intersection and the base locus scheme of [Formula: see text] is smooth, or (ii) [Formula: see text] is a hypersurface.

AN EXHAUSTIVE LIST OF COMPLETE INTERSECTION CALABI-YAU MANIFOLDS

1994 ◽  
Vol 09 (24) ◽  
pp. 2235-2243 ◽  
Author(s):  
M. GAGNON ◽  
Q. HO-KIM
Keyword(s):  
Complete Intersection ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Euler Numbers ◽  
Cartesian Products ◽  
Complex Projective Spaces ◽  
Complex Projective ◽  
Exhaustive List ◽  
Calabi Yau Manifolds

We have obtained a new list of Calabi-Yau manifolds realized as complete intersections of polynomials in Cartesian products of complex projective spaces. It contains 97,360 configurations with Euler numbers ranging from 0 to −200. A remarkable structure emerges from this compilation.

scholarly journals Mazur’s rational torsion result for pointless genus one curves: examples

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Arjan Dwarshuis ◽  
Majken Roelfszema ◽  
Jaap Top
Keyword(s):  
Algebraic Geometry ◽  
Elliptic Curves ◽  
Rational Point ◽  
Torsion Points ◽  
Arbitrary Genus ◽  
Mazur’S Theorem ◽  
Genus One

AbstractThis note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over $$\mathbb {Q}$$ Q in a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point. The main result is that explicit examples are provided of ‘pointless’ genus one curves over $$\mathbb {Q}$$ Q corresponding to the torsion orders 7, 8, 9, 10, 12 (and hence, all possibilities) occurring in Mazur’s theorem. In fact three distinct methods are proposed for constructing such examples, each involving different in our opinion quite nice ideas from the arithmetic of elliptic curves or from algebraic geometry.

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 ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES

2016 ◽  
Vol 222 (1) ◽  
pp. 186-209
Author(s):  
RYOSUKE TAKAHASHI
Keyword(s):  
Vector Field ◽  
Recent Work ◽  
Projective Spaces ◽  
Ricci Soliton ◽  
Complete Intersections ◽  
Necessary Condition ◽  
Ricci Solitons ◽  
Fano Varieties ◽  
Holomorphic Vector Field ◽  
Fano Manifold

Let $M$ be a Fano manifold. We call a Kähler metric ${\it\omega}\in c_{1}(M)$ a Kähler–Ricci soliton if it satisfies the equation $\text{Ric}({\it\omega})-{\it\omega}=L_{V}{\it\omega}$ for some holomorphic vector field $V$ on $M$. It is known that a necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian and Zhu. In a recent work of Berman and Nyström, it was generalized for (possibly singular) Fano varieties, and the notion of algebrogeometric stability of the pair $(M,V)$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

scholarly journals Complete intersections primitive structures on space curves

2015 ◽  
Vol 26 (12) ◽  
pp. 1550104
Author(s):  
Philippe Ellia
Keyword(s):  
Complete Intersection ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Complete Intersections ◽  
Multiple Structure ◽  
Space Curves ◽  
Structure Formula ◽  
Primitive Structure

A multiple structure [Formula: see text] on a smooth curve [Formula: see text] is said to be primitive if [Formula: see text] is locally contained in a smooth surface. We give some numerical conditions for a curve [Formula: see text] to be a primitive set theoretical complete intersection (i.e. to have a primitive structure which is a complete intersection).

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