Related papers: Manin's b-constant in families

We prove that Bernoulli convolutions are absolutely continuous provided the parameter lambda is an algebraic number sufficiently close to 1 depending on the Mahler measure of lambda.

We prove that Behrend's function is constant on Hilb^n(C^3). A calculation of motivic zeta functions shows the relevant Milnor fibers have zero Euler characteristic. As a corollary we see that Hilb^n(C^3) is generically reduced. These…

We prove the Batyrev-Manin conjecture for smooth equivariant compactifications of forms of $\mathbb{G}_a^n$ over a global function field $F$, assuming some conditions on the boundary divisor. To verify that the leading constant agrees with…

In this paper we disprove the following conjectured generalization of the Contraction Mapping Theorem (due to J.D. Stein Jr.): Let X be a complete metric space and let F be a finite family of self-maps of X. Suppose there is a postive…

We investigate Manin's conjecture for del Pezzo surfaces of degree five with a conic bundle structure, proving matching upper and lower bounds, and the full conjecture in the Galois general case.

Let C_n(M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H_i(C_n(M); Q) are representation stable in the sense of [Church-Farb].…

We extend an argument of Stoppa to make some prgress towards a proof that K\"ahler-Einstein manifolds are "b-stable". We point out some algebro-geometric questions, involving finite generation, that arise.

Following the line of attack from La Bret\`eche, Browning and Peyre, we prove Manin's conjecture in its strong form conjectured by Peyre for a family of Ch\^atelet surfaces which are defined as minimal proper smooth models of affine…

Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety in terms of its global geometric invariants. The strongest form of the conjecture implies certain…

We prove two results about generically stable types $p$ in arbitrary theories. The first, on existence of strong germs, generalizes results from D. Haskell, E. Hrushovski and D. Macpherson on stably dominated types. The second is an…

We observe what the canonical bundle formula gives towards a conjecture of Schnell on algebraic fiber spaces, a question concerning the equivalence between the non-vanishing conjecture and the Campana--Peternell conjecture. As a result, we…

We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally,…

In this paper we consider the Holm-Staley $b$-family of equations in the Sobolev spaces $H^s(\mathbb R)$ for $s > 3/2$. Using a geometric approach we show that, for any value of the parameter $b$, the corresponding solution map,$u(0)…

This paper presents our proof of the "strong Macdonald constant term conjecture" of P. Hanlon and B. Feigin.

We give a short proof of a conjecture of Lubin concerning certain families of $p$-adic power series that commute under composition. We prove that if the family is full (large enough), there exists a Lubin-Tate formal group such that all the…

We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].

Mubayi's Conjecture states that if $\mathcal{F}$ is a family of $k$-sized subsets of $[n] = \{1,\ldots,n\}$ which, for $k \geq d \geq 2$, satisfies $A_1 \cap\cdots\cap A_d \neq \emptyset$ whenever $|A_1 \cup\cdots\cup A_d| \leq 2k$ for all…

We study the (trace) norm of a linearly invariant family in the ball in $\C$. By adapting an approach that in one variable yields optimal results, we are able to derive an upper bound for the norm of the family in terms of the Schwarzian…

In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.

A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair (curve, line bundle).