Toric construction and Chow ring of moduli space of quasi maps from ℙ1 with two marked points to ℙ1 × ℙ1

2020 ◽  
Vol 31 (12) ◽  
pp. 2050094
Author(s):  
Kohki Matsuzaka
Keyword(s):  
Moduli Space ◽  
Lower Degree ◽  
Chow Ring ◽  
Poincaré Polynomial ◽  
Marked Points

In this paper, we present explicit toric construction of moduli space of quasi maps from [Formula: see text] with two marked points to [Formula: see text], which was first proposed by Jinzenji and prove that it is a compact orbifold. We also determine its Chow ring and compute its Poincaré polynomial for some lower degree cases.

Chow rings of Mp̃0,2(N,d) and M¯0,2(ℙN−1,d) and Gromov–Witten invariants of projective hypersurfaces of degree 1 and 2

2017 ◽  
Vol 28 (12) ◽  
pp. 1750090 ◽  
Author(s):  
Hayato Saito
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Intersection Number ◽  
Witten Invariant ◽  
Chow Ring ◽  
Stable Curves ◽  
Chow Rings ◽  
Number Formula ◽  
Genus Formula ◽  
Marked Points

In this paper, we prove formulas that represent two-pointed Gromov–Witten invariant [Formula: see text] of projective hypersurfaces with [Formula: see text] in terms of Chow ring of [Formula: see text], the moduli spaces of stable maps from genus [Formula: see text] stable curves to projective space [Formula: see text]. Our formulas are based on representation of the intersection number [Formula: see text], which was introduced by Jinzenji, in terms of Chow ring of [Formula: see text], the moduli space of quasi maps from [Formula: see text] to [Formula: see text] with two marked points. In order to prove our formulas, we use the results on Chow ring of [Formula: see text], that were derived by Mustaţǎ and Mustaţǎ. We also present explicit toric data of [Formula: see text] and prove relations of Chow ring of [Formula: see text].

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 Intersection Poincaré Polynomial for Nagaraj-Seshadri moduli space

2017 ◽  
Vol 291 (1) ◽  
pp. 7-23 ◽  
Author(s):  
Pabitra Barik ◽  
Arijit Dey ◽  
B. N. Suhas
Keyword(s):  
Moduli Space ◽  
Poincaré Polynomial

scholarly journals Gaps of saddle connection directions for some branched covers of tori

2021 ◽  
pp. 1-55
Author(s):  
ANTHONY SANCHEZ
Keyword(s):  
Moduli Space ◽  
Saddle Connection ◽  
Branched Covers ◽  
Translation Surfaces ◽  
Horocycle Flow ◽  
Return Times ◽  
Marked Points ◽  
Specific Orientation

Abstract We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at zero and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points with a specific orientation. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space.

scholarly journals Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

2016 ◽  
Vol 2016 (8) ◽  
Author(s):  
Vittorio Del Duca ◽  
Stefan Druc ◽  
James Drummond ◽  
Claude Duhr ◽  
Falko Dulat ◽  
...  
Keyword(s):  
Moduli Space ◽  
Marked Points

scholarly journals Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points

2014 ◽  
Vol 25 (14) ◽  
pp. 1450125 ◽  
Author(s):  
Marina Logares ◽  
Vicente Muñoz
Keyword(s):  
Elliptic Curve ◽  
Moduli Space ◽  
Betti Numbers ◽  
Conjugacy Classes ◽  
Character Variety ◽  
Higgs Bundles ◽  
Hodge Numbers ◽  
Hodge Polynomials ◽  
Marked Points

We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

scholarly journals The vanishing of the chow cohomology ring for affine toric varieties and additional results

2019 ◽  
Author(s):  
◽  
Ryan Matthew Richey
Keyword(s):  
Recent Work ◽  
Moduli Space ◽  
Toric Variety ◽  
Cohomology Ring ◽  
Toric Varieties ◽  
Chow Ring

From the recent work of Edidin and Satriano, given a good moduli space morphism between a smooth Artin stack and its good moduli space X, they prove that the Chow cohomology ring of X embeds into the Chow ring of the stack. In the context of toric varieties, this implies that the Chow cohomology ring of any toric variety embeds into the Chow ring of its canonical toric stack. Furthermore, the authors give a conjectural description of the image of this embedding in terms of strong cycles. One consequence of their conjectural description, and an additional conjecture, is that the Chow cohomology ring of any affine toric variety ought to vanish. We prove this result without any assumption on smoothness. Afterwards, we present a series of results related to their conjectural description, and finally, we provide a conjectural toric description of the image of this embedding for complete toric varieties by utilizing Minkowski weights.

scholarly journals The Chow ring of the moduli space of curves of genus six

2015 ◽  
Vol 2 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Nikola Penev ◽  
Ravi Vakil
Keyword(s):  
Moduli Space ◽  
Moduli Space Of Curves ◽  
Chow Ring
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