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Showing 1 to 20 of 55 for “"Moduli spaces"”.
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Operads and moduli spaces
… operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics. We consider the extension of classical 2-dimensional …
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Homotopy theory of moduli spaces
… is the study of Maurer-Cartan elements and their moduli spaces, that is their study up to homotopy or gauge equivalence. Within the three papers cited above (and thus within this thesis), three different applications of Maurer-Cartan elements are demonstrated. The first application constructs …
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Toric Varieties Associated with Moduli Spaces
… (S1)3 g-3+n' on an open dense subset of the moduli space of certain gauge equivalence classes of flat SU(2)-connections on Σg,n. Jeffrey and Weitsman also provide a complete description of the moment polytopes for these torus actions, and we make use of this description to study the …
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Moduli spaces of rational graphically stable curves
… condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. …
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Moduli Spaces of Dynamical Systems on Pn
This thesis studies the space of morphisms on Pn defined by polynomials of degree d and its quotient by the conjugation action of PGL(n+1), which should be thought of as coordinate change. First, we construct the quotient using geometric invariant theory, proving that it is a geometric quotient and …
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Bubble tree compactification of instanton moduli spaces
We study the compactification of moduli spaces defined by the anti-self-dual (ASD) Yang-Mills equations on SU(2) or SO(3) bundles over closed oriented Riemannian 4-manifolds and 4-orbifolds. In general the ASD moduli space is not compact since the curvature of a sequence of connections may blow up …
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Bubble tree compactification of instanton moduli spaces
We study the compactification of moduli spaces defined by the anti-self-dual (ASD) Yang-Mills equations on SU(2) or SO(3) bundles over closed oriented Riemannian 4-manifolds and 4-orbifolds. In general the ASD moduli space is not compact since the curvature of a sequence of connections may blow up …
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Shifted symplectic structures and derived moduli spaces
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms
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Moduli spaces and cw structures arising from morse theory
<p>In this dissertation, we study the moduli spaces and CW Structures arising from Morse theory.</p> <p>Suppose M is a smooth manifold and f is a Morse function on it. We consider the negative gradient flow of f. Suppose the flow satisfies transversality. This naturally defines the moduli spaces of …
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On the Riemannian geometry of Seiberg-Witten moduli spaces
… for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an L2-metric on Yang-Mills moduli spaces as …
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High genus moduli spaces in closed string field theory
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1997.
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Explicit moduli spaces for curves of genus 1 and 2
… as Galois modules. In particular, we study the moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces …
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Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces
… two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. The problem boils down to the construction of a …
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On the geometry and topology of moduli spaces of multi-polygonal linkages
… topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and …
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The tautological classes of the moduli spaces of stable maps to flag varieties
… the tautological classes of the Kontsevich-Manin moduli spaces of genus 0 stable maps to SL flag varieties. We prove that the rational cohomology and rational Chow rings of these spaces are isomorphic and that they are generated by tautological classes. In the case when the target is a projective …
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Topology and combinatorics of low genus mapping spaces to projective space
… and boundary combinatorics of two classes of moduli spaces parametrising maps from elliptic curves to projective space - the Vakil--Zinger space and Kontsevich stable map spaces - combining the techniques of mixed Hodge structures, tropical moduli spaces, symmetric functions, and the …
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Geometry of logarithmic mapping spaces in genus one
… we explore several parts of the geometry of the moduli spaces of genus one logarithmic stable maps. In Chapter 2, we exhibit a smooth compactification of the moduli space of elliptic curves in a product of projective spaces with tangency along a subset of its toric boundary divisors. This is a …
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Enumerative invariants for local Calabi-Yau threefolds
… the topological Euler characteristics of the moduli spaces of stable sheaves of dimension one on the total space of rank 2 bundle on P1 whose determinant is O(−2). We count the torus fixed stable sheaves of low degrees and show the results verify the predictions in physics and the local …
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Rational families of vector bundles on curves
… components of the space of rational curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the maximally rationally connected quotient of such a component is either the Jacobian J(C) or a direct sum of …
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