Genera of curves on a very general surface in P3P^3

In this paper we consider the question of determining the geometric genera of irreducible curves lying on a very general surface $S$ of degree $d$ at least 5 in $\mathbb{P}^3$ (the cases $d \leqslant 4$ are well known). We introduce the set $Gaps(d)$ of all non-negative integers which are not realized as geometric genera of irreducible curves on $S$. We prove that $Gaps(d)$ is finite and, in particular, that $Gaps(5)= \{0,1,2\}$. The set $Gaps(d)$ is the union of finitely many disjoint and separated integer intervals. The first of them, according to a theorem of Xu, is $Gaps_0(d):=[0, \frac{d(d-3)}{2} - 3]$. We show that the next one is $Gaps_1(d):= [\frac{d^2-3d+4}{2}, d^2-2d-9]$ for all $d \geqslant 6$.Comment: 16 page

FAKTOR-FAKTOR YANG MEMPENGARUHI EFEKTIVITAS GABUNGAN KELOMPOK TANI (GAPOKTAN) DALAM PROGRAM PENGEMBANGAN USAHA AGRIBISNIS PERDESAAN (PUAP) DI KECAMATAN PEDAN KABUPATEN KLATEN

n this paper we give the full classification of curves $C$ of genus $g$ such that a Brill--Noether locus $W^ s_d(C)$, strictly contained in the jacobian $J(C)$ of $C$, contains a variety $Z$ stable under translations by the elements of a positive dimensional abelian subvariety $A\subsetneq J(C)$ and such that $\dim(Z)=d-\dim(A)-2s$, i.e., the maximum possible dimension for such a $Z$

Electrical noise properties in aging materials

The electric thermal noise has been measured in two aging materials, a colloidal suspension (Laponite) and a polymer (polycarbonate), presenting very slow relaxation towards equilibrium. The measurements have been performed during the transition from a fluid-like to a solid-like state for the gel and after a quench for the polymer. For both materials we have observed that the electric noise is characterized by a strong intermittency, which induces a large violation of the Fluctuation Dissipation Theorem (FDT) during the aging time, and may persist for several hours at low frequency. The statistics of these intermittent signals and their dependance on the quench speed for the polymer or on sample concentration for the gel are studied. The results are in a qualitative agreement with recent models of aging, that predict an intermittent dynamics.Comment: SPIE Proceeding Journa

Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation constant in the system, exploiting the Fluctuation-Dissipation Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT) additionally describe symmetry properties of the probability density functions (PDFs) of the fluctuations of injected and dissipated energies. We experimentally probe a model system: an electrical dipole driven out of equilibrium by a small constant current $I$, and show that FT are experimentally accessible and valid. Furthermore, we stress that FT can be used to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just studying the PDFs symmetries.Comment: Juillet 200

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

Failure time and critical behaviour of fracture precursors in heterogeneous materials

The acoustic emission of fracture precursors, and the failure time of samples of heterogeneous materials (wood, fiberglass) are studied as a function of the load features and geometry. It is shown that in these materials the failure time is predicted with a good accuracy by a model of microcrack nucleation proposed by Pomeau. We find that the time interval $$ between events (precursors) and the energy $\varepsilon$ are power law distributed and that the exponents of these power laws depend on the load history and on the material. In contrast, the cumulated acoustic energy $E$ presents a critical divergency near the breaking time $\tau$ which is % E\sim \left( \frac{\tau -t}\tau \right) ^{-\gamma }. The positive exponent $$ is independent, within error bars, on all the experimental parameters.Comment: to be published on European Physical Journa

Lines, conics, and all that

34 pp.This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc

On Fano schemes of complete intersections

Added lacking references, corrected acknowledgments, minor editorial changesWe provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete intersection is irregular of dimension at least 2, and for the Fano surfaces we deduce formulas for their holomorphic Euler characteristic

Decomposition of homogeneous polynomials with low rank

Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^{{m+d\choose d}-1}$ but that its minimal decomposition as a sum of $d$-th powers of linear forms $M_1, ..., M_r$ is $F=M_1^d+... + M_r^d$ with $r>s$. We show that if $s+r\leq 2d+1$ then such a decomposition of $F$ can be split in two parts: one of them is made by linear forms that can be written using only two variables, the other part is uniquely determined once one has fixed the first part. We also obtain a uniqueness theorem for the minimal decomposition of $F$ if the rank is at most $d$ and a mild condition is satisfied.Comment: final version. Math. Z. (to appear