Moduli of algebraic curves
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The moduli space of twisted canonical divisors Open
ISSN:1474-7480
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Flat monodromies and a Moduli Space Size Conjecture Open
We investigate how super-Planckian axions can arise when type IIB 3-form flux is used to restrict a two-axion field space to a one-dimensional winding trajectory. If one does not attempt to address notoriously complicated issues like Kahle…
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Ends of the moduli space of Higgs bundles Open
We associate to each stable Higgs pair $(A_0,\\Phi_0)$ on a compact Riemann\nsurface $X$ a singular limiting configuration $(A_\\infty,\\Phi_\\infty)$,\nassuming that $\\det \\Phi$ has only simple zeroes. We then prove a\ndesingularization…
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A new cohomology class on the moduli space of curves Open
We define a collection $\Theta_{g,n}\in H^{4g-4+2n}(\overline{\cal M}_{g,n},\mathbb{Q})$ for $2g-2+n>0$ of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers $\int_{\overline{\cal M}_{g,…
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Kink moduli spaces: Collective coordinates reconsidered Open
Moduli spaces - finite-dimensional, collective coordinate manifolds - for\nkinks and antikinks in $\\phi^4$ theory and sine-Gordon theory are reconsidered.\nThe field theory Lagrangian restricted to moduli space defines a reduced\nLagrangi…
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Quintessence and the Swampland: The Parametrically Controlled Regime of Moduli Space Open
We provide evidence that slow roll is not possible in any parametrically controlled regime of the moduli space of string theory. This is proven in full generality in the asymptotic limit of the moduli space of type II and heterotic Calabi‐…
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Cubic curves and totally geodesic subvarieties of moduli space Open
In this paper we present the first example of a primitive, totally geodesic subvariety F⊂g,nF⊂Mg,n with dim(F)>1dim(F)>1. The variety we consider is a surface F⊂1,3F⊂M1,3 defined using the projective geometry of plane cubic curves. We al…
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Homological stability for moduli spaces of high dimensional manifolds. II Open
We prove a homological stability theorem for moduli spaces of manifolds of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies of S$^\textit{n}$…
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Moduli stacks of semistable sheaves and representations of Ext–quivers Open
We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext–quivers with convergent relations. When the …
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Dimension Theory of the Moduli Space of Twisted $K$-Differentials Open
In this note we extend the dimension theory for the spaces \widetilde{\mathcal{H}}_g^k(\mu) of twisted k -differentials defined by Farkas and Pandharipande in [G. Farkas and R. Pandharipande, J. Inst. Math. Jussieu 17, No. 3, 615–672 (2018…
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Moduli of stable maps in genus one and logarithmic geometry, I Open
This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus [math] . We construct a smooth and proper moduli space dominating the main component of Kon…
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All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space Open
We present a twistorlike formula for the complete tree-level S matrix of six-dimensional (6D) (2,0) supergravity coupled to 21 Abelian tensor multiplets. This is the low-energy effective theory that corresponds to type IIB superstring theo…
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The moduli space of multi-scale differentials Open
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with nor…
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Bulk reconstruction in moduli space holography Open
A bstract It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-m…
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Enhancements in F-theory models on moduli spaces of K3 surfaces with ADE rank 17 Open
We study the moduli of elliptic K3 surfaces with a section with the $ADE$\nrank 17. While the Picard number of a generic K3 surface in such moduli space\nis 19, the Picard number is enhanced to 20 at special points in the moduli. K3\nsurfa…
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Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold Open
We use numerical methods to obtain moduli-dependent Calabi-Yau metrics, and from them, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distanc…
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Wall crossing for K-moduli spaces of plane curves Open
We construct proper good moduli spaces parametrizing K-polystable $\mathbb{Q}$-Gorenstein smoothable log Fano pairs $(X, cD)$, where $X$ is a Fano variety and $D$ is a rational multiple of the anti-canonical divisor. We then establish a wa…
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Compactifications of moduli of elliptic K3 surfaces: Stable pair and toroidal Open
We describe two geometrically meaningful compactifications of the moduli\nspace of elliptic K3 surfaces via stable slc pairs, for two different choices\nof a polarizing divisor, and show that their normalizations are two different\ntoroida…
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Genus stabilization for the components of moduli spaces of curves with symmetries Open
In a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\\e$ for the faithful action of a finite group G on an algebraic curve. \nWe show here that the moduli space of curves admitting a faithful action of a finite…
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The tadpole problem Open
A bstract We examine the mechanism of moduli stabilization by fluxes in the limit of a large number of moduli. We conjecture that one cannot stabilize all complex-structure moduli in F-theory at a generic point in moduli space (away from s…
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The tadpole conjecture in the interior of moduli space Open
A bstract We revisit moduli stabilization on Calabi-Yau manifolds with a discrete symmetry. Invariant fluxes allow for a truncation to a symmetric locus in complex structure moduli space and hence drastically reduce the moduli stabilizatio…
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Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces Open
This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of …
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The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves Open
We bound from below the complexity of the top Chern class $\lambda _g$ of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas for $\lambda _g$ in terms of classes of degrees 1 and 2 can exist. As a consequence of t…
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Double ramification cycles on the moduli spaces of curves Open
Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to th…
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Moduli spaces of rank 2 instanton sheaves on the projective space Open
We study the irreducible components of the moduli space of instanton sheaves\non $\\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with\n$c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we\nclassify all instant…
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The Moduli Space of Two-Convex Embedded Tori Open
EPSRC [EP/M011224/1 to R.B.]; NSERC [RGPIN-2016-04331], NSF [DMS-1406394], and a Connaught New Researcher Award (to R.H.); AMS-Simons travel grant (to O.H.).
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Moduli spaces and macromolecules Open
Techniques from moduli spaces are applied to biological macromolecules. The first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally. The second main result identifies up …
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Remarks on motives of moduli spaces of rank 2 vector bundles on curves Open
Let $C$ be an algebraic curve of genus $g \geq 2$ and $M_L$ be the moduli space of rank 2 stable vector bundles on $C$ whose determinants are isomorphic to a fixed line bundle $L$ of degree 1 on $C.$ S. del Bano studied motives of moduli s…
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Integrability, Quantization and Moduli Spaces of Curves Open
This paper has the purpose of presenting in an organic way a new approach to\nintegrable (1+1)-dimensional field systems and their systematic quantization\nemerging from intersection theory of the moduli space of stable algebraic\ncurves a…
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Black holes as probes of moduli space geometry Open
A bstract We argue that supersymmetric BPS states can act as efficient finite energy probes of the moduli space geometry thanks to the attractor mechanism. We focus on 4d $$ \mathcal{N} $$ = 2 compactifications and capture aspects of the e…