Quasi-Jacobi forms, elliptic genera and strings in four dimensions [PDF]
Journal of High Energy Physics, 2021 We investigate the interplay between the enumerative geometry of Calabi-Yau fourfolds with fluxes and the modularity of elliptic genera in four-dimensional string theories.
Seung-Joo Lee +3 more
semanticscholar +2 more sources
Floor diagrams and enumerative invariants of line bundles over an elliptic curve [PDF]
Compositio Mathematica, 2021 We use the tropical geometry approach to compute absolute and relative enumerative invariants of complex surfaces which are $\mathbb {C} P^1$-bundles over an elliptic curve.
Thomas Blomme
semanticscholar +1 more source
Quasi-inner automorphisms of Drinfeld modular groups [PDF]
Groups, Geometry, and Dynamics, 2021 Let $A$ be the set of elements in an algebraic function field $K$ over ${\mathbb F}_q$ which are integral outside a fixed place $\infty$. Let $G=GL_2(A)$ be a {\it Drinfeld modular group}.
A. Mason, A. Schweizer
semanticscholar +1 more source
Coxeter group in Hilbert geometry [PDF]
, 2015 A theorem of Tits - Vinberg allows to build an action of a Coxeter group $\Gamma$ on a properly convex open set $\Omega$ of the real projective space, thanks to the data $P$ of a polytope and reflection across its facets.
Marquis, Ludovic
core +3 more sources
Variational quasi-harmonic maps for computing diffeomorphisms
ACM Transactions on Graphics, 2023 Computation of injective (or inversion-free) maps is a key task in geometry processing, physical simulation, and shape optimization. Despite being a longstanding problem, it remains challenging due to its highly nonconvex and combinatoric nature.
Yu Wang, Minghao Guo, J. Solomon
semanticscholar +1 more source
On the nature of isolated asymptotic singularities of solutions of a family of quasi-linear elliptic PDE's on a Cartan–Hadamard manifold [PDF]
Communications in analysis and geometry, 2016 Let $M$ be a Cartan-Hadamard manifold with sectional curvature satisfying $-b^2\leq K\leq -a^2 0.$ Denote by $\partial_{\infty}M$ the asymptotic boundary of $M$ and by $\bar M:= M\cup\partial_\infty M$ the geometric compactification of $M$ with the cone ...
L. Bonorino, J. Ripoll
semanticscholar +1 more source
Numerical implementation of isolated horizon boundary conditions [PDF]
, 2006 We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium.
A. Ashtekar +3 more
core +4 more sources
On the Quasi-linear Elliptic PDE $${-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}}$$ in Physics and Geometry [PDF]
, 2011 It is shown that for each finite number N of Dirac measures $${\delta_{s_n}}$$ supported at points $${s_n \in {\mathbb R}^3}$$ with given amplitudes $${a_n \in {\mathbb R} \backslash\{0\}}$$ there exists a unique real-valued function $${u \in C^{0, 1 ...
M. Kiessling
semanticscholar +1 more source
Quasi-modular forms attached to elliptic curves, I [PDF]
, 2011 In the present text we give a geometric interpretation of quasi-modular forms using moduli of elliptic curves with marked elements in their de Rham cohomologies.
Movasati, Hossein
core +2 more sources
Gromov–Witten theory of elliptic fibrations : Jacobi forms and holomorphic anomaly equations [PDF]
Geometry and Topology, 2017 We conjecture that the relative Gromov-Witten potentials of elliptic fibrations are (cycle-valued) lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation.
G. Oberdieck, A. Pixton
semanticscholar +1 more source