Related papers: Distinguished Line Bundles for Complex Surface Aut…

We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles…

We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of…

We study holomorphic automorphisms on compact K\"ahler manifolds having simple actions on the Hodge cohomology ring. We show for such automorphisms that the main dynamical Green currents admit complex laminar structures (woven currents) and…

We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any…

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.

In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a (-2)-curve. Then we show that this equivalence gives another…

We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…

We extend to arbitrary characteristic some known results about automorphisms of complex Enriques surfaces that act trivially on the cohomology or the cohomology modulo torsion.

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

The automorphism group of a projective bundle P(E) over a simplicial toric variety is described when the bundle E is a direct sum of line bundles. Applications to study of moduli of complete intersections on toric varieties, including…

Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in…

We classify two-dimensional complex tori admitting automorphisms with positive entropy in terms of the entropies they exhibit. For each possible positive value of entropy, we describe the set of two-dimensional complex tori admitting…

In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.

We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if…

We prove a number of results to the general effect that, under obviously necessary numerical and determinant constraints, "most" morphisms between fixed bundles on a complex elliptic curve produce (co)kernels which can either be specified…