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The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...
We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...
Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...
Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's ...
Since their discovery, carbon nanotubes (CNTs) have attracted intense attention to broad range of potential applications. In contrast to the 1D isolated single-walled carbon nanotubes (SWCNT), 2D films or bundles made of thousands of tubes have been introd ...
We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...
Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...
We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...
We prove that one can run the log minimal model program for log canonical 3-fold pairs in characteristic p > 5. In particular, we prove the cone theorem, contraction theorem, the existence of flips and the existence of log minimal models for pairs with log ...
In this work, the influence of ply thickness on strain energy release rate (ERR) in delamination of carbon epoxy laminates is addressed. Specimens with three ply thicknesses: 0.030, 0.075 and 0.150 mm are tested. While the ERR at onset of crack propagation ...
