Published in Advances in Mathematics
We introduce various families of irreducible homaloidal hypersurfaces in projective space P r , for all r ⩾ 3 . Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the c...
Published in Advances in Mathematics
We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described both explicitly and from an infinite dimensional viewpoint (generalising the Atiyah–Bott approach). This enab...
Published in Advances in Mathematics
Published in Advances in Mathematics
We prove Viehwegʼs hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the base space of a maximal variation family of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.
Published in Advances in Mathematics
Published in Advances in Mathematics
We iterate Manolescu’s unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over Z/2Z. The result is a spectral sequence which converges to a stabilized version of δ-graded knot Floer homology. The (E2,d2) page of this spectral sequence is an algorithmically computable chain complex expressed i...
Published in Advances in Mathematics
We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of ...
Published in Advances in Mathematics
Motivated by the Broué conjecture on blocks with abelian defect groups for finite reductive groups, we study “parabolic” Deligne–Lusztig varieties and construct on those which occur in the Broué conjecture an action of a braid monoid, whose action on their ℓ-adic cohomology will conjecturally factor through a cyclotomic Hecke algebra. In order to c...
Published in Advances in Mathematics
The main aim of this article is to compute all the moments of the number of pℓ-torsion elements in some type of finite abelian groups. The averages involved in these moments are those defined for the Cohen–Lenstra heuristics for class groups and their adaptation for Tate–Shafarevich groups. In particular, we prove that the heuristic model for Tate–...
Published in Advances in Mathematics
We denote by ConcA the (∨,0)-semilattice of all finitely generated congruences of an (universal) algebra A, and we define ConcV as the class of all isomorphic copies of all ConcA, for A∈V, for any variety V of algebras.Let V and W be locally finite varieties of algebras such that for each finite algebra A∈V there are, up to isomorphism, only finite...
