Related papers: On Iwase's manifolds
The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of…
We conjecture two generalisations of Elkies' theorem on unimodular quadratic forms to non-unimodular forms. We give some evidence for these conjectures including a result for determinant 3. These conjectures, when combined with results of…
We revisit Brunella's proof of the fact that Kato surfaces admit locally conformally K\" ahler metrics, and we show that it holds for a large class of higher dimensional complex manifolds containing a global spherical shell. On the other…
Lov\'asz (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B for any finite structure C. Soon after,…
We demonstrate that M-theory compactifications on 7-manifolds of G_2 holonomy, which yield 4d N=1 supersymmetric systems, often admit at special loci in their moduli space a description as type IIA orientifolds. In this way, we are able to…
We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the…
Using M-theory compactification, we develop a three factor separation for the scalar submanifold of N=2 seven dimensional supergravity associated with 2-cycles of the K3 surface. Concretely, we give an interplay between the three scalar…
We construct a quartic threefold with L-rational singularities which has torsion in its middle homology group. This answers a question of Brown and Schnetz for all fields of characteristic zero.
We introduce "$t$-LC triangulated manifolds" as those triangulations obtainable from a tree of $d$-simplices by recursively identifying two boundary $(d-1)$-faces whose intersection has dimension at least $d-t-1$. The $t$-LC notion…
This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that…
In this paper, we completely classify the isomorphism classes of certain lattices $L_A(C)$ and $L_B(C)$ from a self-orthogonal code $C$ over the finite field $\mathbb{F}_p$, where $p$ is an odd prime. These lattices are obtained by…
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…
Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~M\"oller, from the viewpoint of flat and complex geometry, for the purpose of compactifying moduli spaces of curves together with a…
We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it…
We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the Chern numbers of 3-folds with smooth families of minimal surfaces of general type…
We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4…
We construct nontrivial L-equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L-equivalence for curves (necessarily over…
We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and…
The objective of this thesis is to study the automorphism groups of the Lie algebras attached to linear systems. A linear system is a pair of vector spaces $(U,W)$ with a nondegenerate pairing $\langle\cdot,\cdot\rangle\colon U\otimes W\to…
This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $d+1$, $d\ge3$, the local energy of solutions to the scalar wave equation…