相关论文: Actions of $\mu_p$ on canonically polarized surfac…

Let p be an odd prime, and consider the map H_p which sends an integer x to either x/2 or (px+1)/2 depending on whether x is even or odd. The values at x=0 of arbitrary composition sequences of the maps x/2 and (px+1)/2 can be parameterized…

We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.

In this paper, we study finite symplectic actions on K3 surfaces X, i.e. actions of finite groups G on X which act on H^{2,0}(X) trivially. We show that the action on the K3 lattice H^2(X,Z) induced by a symplectic action of G on X depends…

We prove new $L_p$ affine isoperimetric inequalities for all $ p \in [-\infty,1)$. We establish, for all $p\neq -n$, a duality formula which shows that $L_p$ affine surface area of a convex body $K$ equals $L_\frac{n^2}{p}$ affine surface…

In this paper, we prove the boundedness of foliated surfaces $(X,\mathscr{F})$ which are minimal partial du Val resolutions of canonical models $(X_c,\mathscr{F}_c)$ of general type. For applications, we show the boundedness of non-cusp…

We consider the classical problem of area-preserving maps on annulus $\mathbb{A} = S^1 \times [0, 1]$ . Let $\mathcal{M}_f$ be the set of all invariant probability measures of an area-preserving, orientation preserving diffeomorphism $f$ on…

This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $(\Omega_X^1)^{[\otimes m]}$ has non-zero global sections for some m > 0, where…

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let * be a G-invariant Fedosov star-product on X such that the…

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and $p$-Jordan property. In particular, we show that the Cremona group of rank $2$ over a field of…

Let $k$ be a field of characteristic $p>0$. We discuss the automorphisms of the polynomial ring $k[x_1,\ldots ,x_n]$ of order $p$, or equivalently the ${\bf Z}/p{\bf Z}$-actions on the affine space ${\bf A}_k^n$. When $n=2$, such an…

This paper is motivated by an open question in $p$-adic Fourier theory, that seems to be more difficult than it appears at first glance. Let $L$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $o_L$ and let $\mathbb{C}_p$…

We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable…

Let k be a field of positive characteristic p and let G be a finite group. In this paper we study the category TsG of finitely generated commutative k-algebras A on which G acts by algebra automorphisms with surjective trace. If A = k[X],…

We show, for primes p less than or equal to 13, that a number of well-known MU_(p)-rings do not admit the structure of commutative MU_(p)-algebras. These spectra have complex orientations that factor through the Brown-Peterson spectrum and…

We consider a Hamiltonian action of n-dimensional torus, T^n, on a compact symplectic manifold (M,\omega) with d isolated fixed points. For every fixed point p there exists (though not unique) a class a_p in H^*_{T}(M; Q) such that the…

The generalized Markoff mod $p$ graph is defined via the equation $x^2+y^2+z^2=xyz+\kappa$ over the finite field $\mathbb{F}_p$ of prime order $p$. In this paper, we investigate the topological properties of the graph such as non-planarity,…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

We prove that any $\mathbb{Z}^p$-action ${\bf A}$ that acts by automorphisms of $\mathbb{Z}^q$ with a non-zero fixed-point set induces a unipotent factor of the $\mathbb{Z}^p$-action ${\bf A}$ which determines whether the action ${\bf A}$…

Let D_1 be a subdomain of D_2 in the complex plane CC. Under very mild conditions on D_2 we show that there exist holomorphic functions f, defined on D_1 with the property that $f$ is nowhere extendible across the boundary of D_1, while the…

Minimal algebraic surfaces of general type $X$ such that $K^2_X=2\chi(\mathcal{O}_X)-6$ or $K^2_X=2\chi(\mathcal{O}_X)-5$ are called Horikawa surfaces. In this note we study $\mathbb{Z}^2_2$-actions on Horikawa surfaces. The main result is…