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Showing 1 to 12 of 12 for “"Gromov-Witten theory"”.
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Topics in symplectic Gromov–Witten theory
The main focus of this thesis is on the Gromov--Witten theory of general symplectic manifolds. Mohan Swaminathan and I construct a framework to define a virtual fundamental class for the moduli space of stable maps to a general closed symplectic manifold. Our construction, inspired by [AMS21], …
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Gromov-Witten theory in dimensions two and three
In this thesis, we solve for (equivariant) Gromov-Witten theories of some important classes of surfaces and threefolds, and study their relationships to other brances of mathematics. The first object is the class of P2-bundles over a smooth curve C of genus g. Our bundles are of the form P(L0 + L1 …
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Logarithmic Gromov-Witten theory and double ramification cycles
… Ranganathan), we prove that the logarithmic Gromov-Witten cycles of a toric variety endowed with its toric log structure lie in the tautological subring of the moduli space of stable curves. The result gives a common generalization of work of Faber-Pandharipande, and more recent work of …
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Birational Invariance of Punctured Log Gromov-Witten Theory and Intrinsic Mirror Constructions
… and resolve various problems related to log Gromov-Witten theory and their application to mirror symmetry. We first prove for log Calabi-Yau varieties satisfying a semi-positivity assumption that the Gross-Siebert logarithmic mirror construction encodes solutions to enumerative problems …
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Gromov Witten Invariants of Blow Ups of P² using Logarithmic Geometry
We show that Parker’s recursion for computing Gromov-Witten invariants of blow ups of P² can be derived using logarithmic Gromov-Witten theory and punctured maps. We extend the recursion to compute Gromov-Witten invariants with Hodge class insertions.
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Geometry of logarithmic mapping spaces in genus one
… certain “fictitious” markings, suggesting the theory has good recursive properties. In Chapter 3, we study the desingularized moduli spaces of genus 1 maps to projective spaces in closer detail. This allows us to describe the class of a stratum in the logarithmic moduli spaces by performing …
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Equivariant quantum connections in positive characteristic
… this thesis, we apply techniques from symplectic Gromov--Witten theory to study the equivariant quantum connections in positive characteristic. The main examples of interest arise from symplectic resolutions. We introduce equivariant generalizations of the quantum Steenrod operations of Fukaya, …
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The tautological classes of the moduli spaces of stable maps to flag varieties
… a second proof of this result in the spirit of Gromov-Witten theory by making use of a suitable torus action. In addition, we explicitly describe a Bialynicki-Birula stratification of the Kontsevich-Manin spaces in terms of the Gathmann-Li spaces of relative stable morphisms. Finally, we analyze …
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Quantum Steenrod operations and Fukaya categories
… of mod p equivariant operations to symplectic Gromov-Witten theory has fueled exciting developments in the field. In this thesis, we develop new tools for understanding these operations and explore an application to the quantum connection. In one direction, we construct certain operations on …
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Enumerative invariants for local Calabi-Yau threefolds
… verify the predictions in physics and the local Gromov-Witten theory. In the second part, we compute the Poincar´e polynomial of the moduli space of stable sheaves with Hilbert polynomial 4n + 1 on P2. This is done by classifying all torus fixed points in the moduli space and computing the torus …
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Gross-Siebert Mirror Ring for Smooth log Calabi-Yau Pairs
… paper, we exhibit a formula relating punctured Gromov-Witten invariants used by Gross and Siebert in [GS2] to 2-point relative/logarithmic Gromov-Witten invariants with one point-constraint for any smooth log Calabi-Yau pair (W, D). Denote by Na,b the number of rational curves in W meeting D in …
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Local enumerative invariants of some Gorenstein surfaces and orbifolds
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms