scholarly journals Graph homology of the moduli space of pointed real curves of genus zero

2007 ◽  
Vol 13 (2) ◽  
pp. 203-237 ◽  
Author(s):  
Özgür Ceyhan
Keyword(s):  
Moduli Space ◽  
Genus Zero ◽  
Graph Homology ◽  
Real Curves

scholarly journals NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES

2014 ◽  
Vol 16 (02) ◽  
pp. 1350010 ◽  
Author(s):  
GILBERTO BINI ◽  
FILIPPO F. FAVALE ◽  
JORGE NEVES ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Fundamental Group ◽  
Moduli Space ◽  
General Type ◽  
Picard Number ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Genus Zero ◽  
New Family ◽  
Hodge Numbers ◽  
Projective Lines

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

scholarly journals Relative Quasimaps and Mirror Formulae

2020 ◽  
Author(s):  
Luca Battistella ◽  
Navid Nabijou
Keyword(s):  
Generating Function ◽  
Moduli Space ◽  
Toric Variety ◽  
Recursion Formula ◽  
Genus Zero ◽  
Relative Invariant ◽  
Lefschetz Theorem ◽  
Virtual Class

Abstract We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we show that the relative $I$-function of Fan–Tseng–You coincides with a natural generating function for relative quasimap invariants, providing mirror-symmetric motivation for the theory.

THE (ORBIFOLD) EULER CHARACTERISTIC OF THE MODULI SPACE OF CURVES AND THE CONTINUUM LIMIT OF PENNER'S CONNECTED GENERATING FUNCTION

1991 ◽  
Vol 03 (03) ◽  
pp. 285-300 ◽  
Author(s):  
NOUREDDINE CHAIR
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Euler Characteristic ◽  
Generating Function ◽  
Moduli Space ◽  
Continuum Limit ◽  
Recursion Relation ◽  
Moduli Space Of Curves ◽  
Genus Zero ◽  
The Continuum

The generating function that gives rise to the orbifold Euler characteristic of the moduli space of punctured compact Rieman surfaces [Formula: see text], g ≥ 0 is derived explicitly. In the derivation, we show that we do not need to use the three-term recursion relation for the orthogonal polynomials. Also the continuum limit of Penner's connected generating function is considered and is shown to be formally equivalent to the free energy obtained recently by Distler and Vafa which exhibits the logarithmic divergences found for genus zero and one in D = 1 matrix models. Finally, it is shown that the free energy and its s-derivatives are nothing but the continuum limit of a certain generating function introduced by Harer and Zagier in obtaining the true Euler characteristic with any number of punctures,[Formula: see text], s ≥ 0.

scholarly journals Quantum cohomology of [ℂN/μr]

2010 ◽  
Vol 146 (5) ◽  
pp. 1291-1322 ◽  
Author(s):  
Arend Bayer ◽  
Charles Cadman
Keyword(s):  
Cyclic Group ◽  
Moduli Space ◽  
Chern Class ◽  
Quantum Cohomology ◽  
Closed Formula ◽  
Stable Maps ◽  
Genus Zero ◽  
Witten Theory

AbstractWe give a construction of the moduli space of stable maps to the classifying stack Bμr of a cyclic group by a sequence of rth root constructions on $\overline {M}_{0, n}$. We prove a closed formula for the total Chern class of μr-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus-zero Gromov–Witten theory of stacks of the form [ℂN/μr]. We deduce linear recursions for genus-zero Gromov–Witten invariants.

scholarly journals Counting genus-zero real curves in symplectic manifolds

2016 ◽  
Vol 20 (2) ◽  
pp. 629-695 ◽  
Author(s):  
Mohammad Farajzadeh Tehrani
Keyword(s):  
Symplectic Manifolds ◽  
Genus Zero ◽  
Real Curves

scholarly journals Counting Realizations of Laman Graphs on the Sphere

10.37236/8548 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Matteo Gallet ◽  
Georg Grasegger ◽  
Josef Schicho
Keyword(s):  
Moduli Space ◽  
Explicit Description ◽  
Chow Ring ◽  
Genus Zero ◽  
Stable Curves ◽  
Marked Points

We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space.

scholarly journals Some non-finitely generated Cox rings

2015 ◽  
Vol 152 (5) ◽  
pp. 984-996 ◽  
Author(s):  
José Luis González ◽  
Kalle Karu
Keyword(s):  
Moduli Space ◽  
Smooth Point ◽  
Large Family ◽  
Projective Planes ◽  
Finitely Generated ◽  
Genus Zero ◽  
Cox Rings ◽  
Cox Ring

We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space$\overline{M}_{0,n}$of stable$n$-pointed genus-zero curves does not have a finitely generated Cox ring if$n$is at least$13$.

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