The principal degenerations of abelian surfaces and their polarisations.
The principle of moduli flexibility for real algebraic manifolds
Given a real closed field R, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some Rⁿ. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: "The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters".
The probability that a complete intersection is smooth
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection...
The product of linear forms in a field of series and the Riemann hypothesis for curves
The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
The projectivity of the moduli space of stable curves, II: The stacks M...
The projectivity of the moduli space of stable curves, III: The line bundles on M..., and a proof of the projectivity of M... in characteristic 0.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
The Prym variety for a cyclic unramified cover of a hyperelliptic Riemann surface.
The Prym vector bundle and Gunning vector bundle over the Teichmüller space.
The push-forward and Todd class of flag bundles
The Quadratic Schur Subgroup over Local and Global Fields.
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The Radius of Convergence of Poincaré Series of Loop Spaces.
The Ramification Divisors for Branched Coverings of IP nk.
The rank of étale cohomology of varieties over -adic or number fields
The rank of hyperelliptic Jacobians in families of quadratic twists
The variation of the rank of elliptic curves over in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over admits infinitely many quadratic twists of rank . Most elliptic curves have even infinitely many twists of rank and examples of elliptic curves with infinitely many twists of rank are known. There are also certain density results. This paper studies the variation of the...
The rank of the multiplication map for sections of bundles on curves
Sia una curva liscia di genere ed , fasci coerenti su . Sia l'applicazione di moltiplicazione. Qui si dimostra che ha rango massimo se e è un fibrato stabile generico su . Diamo un'interpretazione geometrica dell'eventuale non-surgettività di quando sono fibrati in rette generati da sezioni globali e . Studiamo anche il caso .
The rank-one limit of the Fourier-Mukai transform.
The rational homotopy theory of smooth, complex projective varieties