Manuscripta Mathematica最新文献

Generalizing the definitions originally presented by Kuznetsov and Faenzi, we study (possibly non locally free) instanton sheaves of arbitrary rank on Fano threefolds. We classify rank 1 instanton sheaves and describe all curves whose structure sheaves are rank 0 instanton sheaves. In addition, we show that every rank 2 instanton sheaf is an elementary transformation of a locally free instanton sheaf along a rank 0 instanton sheaf. To complete the paper, we describe the moduli space of rank 2 instanton sheaves of charge 2 on a quadric threefold X and show that the full moduli space of rank 2 semistable sheaves on X with Chern classes ((c_1,c_2,c_3)=(-,1,2,0)) is connected and contains, besides the instanton component, just one other irreducible component which is also fully described.

In this paper, we study the Yau sequence concerning the minimal cycle over complete intersection surface singularities of Brieskorn type, and consider the relations between the minimal cycle A and the fundamental cycle Z. Further, we also give the coincidence between the canonical cycles and the fundamental cycles from the Yau sequence concerning the minimal cycle.

We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian–Sobolev space). Our result covers first-order Sobolev spaces of exponent (pin (1,infty )), defined over a complete separable metric space endowed with a boundedly-finite Borel measure. Our proof is based on a completely smooth analysis: first we reduce the problem to the Banach space setting, where we consider smooth functions instead of Lipschitz ones, then we rely on classical tools in convex analysis and on the superposition principle for normal 1-currents. Along the way, we obtain a new proof of the density in energy of smooth cylindrical functions in Sobolev spaces defined over a separable Banach space endowed with a finite Borel measure.

Let (f: X rightarrow C) be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let (j: J rightarrow C) be the Jacobian fibration of f. In this paper, we prove that the Chow motives of X and J are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch–Kas–Lieberman’s result to arbitrary characteristic.

In this paper we further develop the ideas from Geometric Function Theory initially introduced in Avelin et al. (Commun Math Phys 404:401–437, 2023), to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First, the graph theoretical connection enables us to exactly compute the pre-factor in the capacity. Second, we complete the method from Avelin et al. (Commun Math Phys 404:401–437, 2023) by providing an upper bound using Geometric Function Theory together with Thompson’s principle, avoiding explicit constructions of test functions.

In this paper, we show that complete Bach-flat Schouten solitons with (nge 4) are rigid. When (n=3) we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for (nge 3).

Let X be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves (R^if_*Omega ^p_{tilde{X}}(log E)), where (f: tilde{X} rightarrow X) is a strong log resolution of singularities with reduced exceptional divisor E. These extend the local vanishing theorem for toric varieties in Mustaţă et al. (J. Inst. Math. Jussieu 19(3):801-819, 2020). Our consideration of these sheaves is motivated by the notion of k-rational singularities introduced by Friedman and Laza (Higher Du Bois and higher rational singularities, 2001). In particular, our results lead to criteria for toric varieties to have k-rational singularities, as defined in Shen et al. (On k-Du Bois and k-rational singularities, 2023).

We give some conditions on a family of abelian covers of ({mathbb P}^1) of genus g curves, that ensure that the family yields a subvariety of ({mathsf A}_g) which is not totally geodesic, hence it is not Shimura. As a consequence, we show that for any abelian group G, there exists an integer M which only depends on G such that if (g >M), then the family yields a subvariety of ({mathsf A}_g) which is not totally geodesic. We prove then analogous results for families of abelian covers of ({tilde{C}}_t rightarrow {mathbb P}^1 = {tilde{C}}_t/{tilde{G}}) with an abelian Galois group ({tilde{G}}) of even order, proving that under some conditions, if (sigma in {tilde{G}}) is an involution, the family of Pryms associated with the covers ({tilde{C}}_t rightarrow C_t= {tilde{C}}_t/langle sigma rangle ) yields a subvariety of ({mathsf A}_{p}^{delta }) which is not totally geodesic. As a consequence, we show that if ({tilde{G}}=(mathbb Z/Nmathbb Z)^m) with N even, and (sigma ) is an involution in ({tilde{G}}), there exists an integer M(N) which only depends on N such that, if ({tilde{g}}= g({tilde{C}}_t) > M(N)), then the subvariety of the Prym locus in ({{mathsf A}}^{delta }_{p}) induced by any such family is not totally geodesic (hence it is not Shimura).

Conformal/anticonformal actions of the quasi-abelian group (QA_{n}) of order (2^n), for (nge 4), on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the (QA_n)-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real Riemann surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper, we consider two cases: either (QA_n) has anticonformal elements or only contains conformal elements.

We study the postcritically finite non-polynomial map (f(x)=frac{1}{(x-1)^2}) over a number field k and prove various results about the geometric (G^{textrm{geom}}(f)) and arithmetic (G^{textrm{arith}}(f)) iterated monodromy groups of f. We show that the elements of (G^{textrm{geom}}(f)) are the ones in (G^{textrm{arith}}(f)) that fix certain roots of unity by assuming a conjecture on the size of (G^{textrm{geom}}_n(f)). Furthermore, we describe exactly for which (a in k) the Arboreal Galois group (G_a(f)) and (G^{textrm{arith}}(f)) are equal.