Higher ramification and varieties of secant divisors on the generic curve

For a smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to completely clarify this problem in the case of the generic curve C of given genus. Using degeneration techniques and a few facts about the birational geometry of moduli spaces of stable pointed curves we determine precisely under which conditions the cycle of e-secant k-planes in non-empty and we compute its dimension. We also precisely determine the dimension of the variety of linear series on C carrying e-secant k-planes. In a different direction, in the last part of the paper we study the distribution of ramification points of the powers of a line bundle on C having prescribed ramification at a given point.Comment: 25 pages. Numerous changes suggested by the referee, several proofs explained in more detail. To appear in the Journal of the London Mathematical Societ

Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols

The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q > P, and the interpolation of LP-sub-Markovian semigroups with Feller semigroups is investigated. The structure of generators of L-p-sub-Markovian semigroups is studied. Subordination in the sense of Bochner is used to discuss the construction of refinements of L-p-sub-Markovian semigroups. The role played by some function spaces which are domains of definition for L-p-generators is pointed out. The problem of regularising powers of generators as well as some perturbation results are discussed

A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality

It has been argued that, underlying M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this letter we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page

The past of Hungarian anthropology and future objectives

The author lists the goals drawn up by Aurél Török upon establishing Hungarian anthropology. Based on these, he first outlines the history of the establishment of university institutes, collections, scientific associations and periodicals, then lists the places and fields of research of Hungarian anthropology. The author describes the connection of Hungarian anthropology with the Hungarian Academy of Sciences and analyses the present state of the new generation of anthropologists. Based on these points the author formulates objectives for the future. Finally, he gives a chronological list of all Hungarian congresses and conferences related to anthropological research.The author lists the goals drawn up by Aurél Török upon establishing Hungarian anthropology. Based on these, he first outlines the history of the establishment of university institutes, collections, scientific associations and periodicals, then lists the places and fields of research of Hungarian anthropology. The author describes the connection of Hungarian anthropology with the Hungarian Academy of Sciences and analyses the present state of the new generation of anthropologists. Based on these points the author formulates objectives for the future. Finally, he gives a chronological list of all Hungarian congresses and conferences related to anthropological research