Focal Varieties of Curves of Genus 6 and 8

In this paper we give a simple Torelli type theorem for curves of genus 6 and 8 by showing that these curves can be reconstructed from their Brill-Noether varieties. Among other results, it is shown that the focal variety of a general, canonical and nonhyperelliptic curve of genus 6 is a hypersurface.Comment: This paper consists of 9 page

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

On the classification of defective threefolds

We classify all irreducible projective threefolds $X$ which are $k$-defective, i.e. some $k$-secant variety of $X$ has dimension less than the expected value. This results extends the classical Scorza's classification of the case $k=1$.Comment: AMSLaTeX, 30 page

On the Severi varieties of surfaces in P^3

The Severi variety V_{n,d} of a smooth projective surface S is defined as the subvariety of the linear system |O_S(n)|, which parametrizes curves with d nodes. We show that, for a general surface S of degree k in P^3 and for all n>k-1, d=0,...,dim(|O_S(n)|), there exists one component of V_{n,d} which is reduced, of the expected dimension dim(|O_S(n)|)-d. Components of the expected dimension are the easiest to handle, trying to settle an enumerative geometry for singular curves on surfaces. On the other hand, we also construct examples of reducible Severi varieties, on general surfaces of degree k>7 in P^3.Comment: AMSTeX, AMSppt style, 14 page

A Series of Smooth Irregular Varieties in Projective Space

One of the simplest examples of a smooth, non degenerate surface in P^4 is the quintic elliptic scroll. It can be constructed from an elliptic normal curve E by joining every point on E with the translation of this point by a non-zero 2-torsion point. The same construction can be applied when E is replaced by a (lineaerly normally embedded) abelian variety A. In this paper we ask the question when the resulting scroll Y is smooth. If A is an abelian surface embedded by a line bundle L of type (d_1,d_2) and r=d_1d_2, then we prove that for general A the scroll Y is smooth if r is at least 7 with the one exception where r=8 and the 2-torsion point is in the kernel K(L) of L. In this case Y is singular.The case r=7 is particularly interesting, since then Y is a smooth threefold in P^6 with irregularity 2. The existence of this variety seems not to have been noticed before. One can also show that the case of the quintic elliptic scroll and the above case are the only possibilities where Y is smooth and the codimension of Y is at most half the dimension of the surrounding projective space.Comment: 23 pages, Plain Tex. Some corrections made. To appear: Annali Sc. Norm. Sup. di Pis

Advanced memory effects in the aging of a polymer glass

A new kind of memory effect on low frequency dielectric measurements on plexiglass (PMMA) is described. These measurements show that cooling and heating the sample at constant rate give an hysteretic dependence on temperature of the dielectric constant $\epsilon$. A temporary stop of cooling produces a downward relaxation of $\epsilon$. Two main features are observed i) when cooling is resumed $\epsilon$ goes back to the values obtained without the cooling stop (i.e. the low temperature state is independent of the cooling history) ii) upon reheating $\epsilon$ keeps the memory of all the cooling stops({\it Advanced memory}). The dependence of this effect on frequency and on the cooling rate is analyzed. The memory deletion is studied too. Finally the results are compared with those of similar experiments done in spin glasses and with the famous experiments of Kovacs.Comment: to be published in the European Physical Journa

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 $Z$