Księdza profesora Kazimierza Waisa propozycja zharmonizowania nauki i wiary w kwestii pochodzenia człowieka

This paper is aimed to present Kazimierz Wais’ considerations on the concept of the origin of man. Kazimierz Wais (1865-1934) was a Polish philosopher and theologian, a professor at the University of L’viv. In his publications, Wais criticized the purely naturalistic theory of the origin of man and presented a positive theory not inconsistent with the Biblical description; he also commented on the issue of the origin of human soul. His views were strongly affected by neo-Thomistic philosophy. The paper shows Wais’ attempts to prove the harmony of science and faith regarding the origin of man. His reflections are presented and critically commented.This paper is aimed to present Kazimierz Wais’ considerations on the concept of the origin of man. Kazimierz Wais (1865-1934) was a Polish philosopher and theologian, a professor at the University of L’viv. In his publications, Wais criticized the purely naturalistic theory of the origin of man and presented a positive theory not inconsistent with the Biblical description; he also commented on the issue of the origin of human soul. His views were strongly affected by neo-Thomistic philosophy. The paper shows Wais’ attempts to prove the harmony of science and faith regarding the origin of man. His reflections are presented and critically commented

Containment problem and combinatorics

In this note, we consider two configurations of twelve lines with nineteen triple points (i.e. points where three lines meet). Both of them have the same arrangemental combinatorial features, which means that in both configurations nine of twelve lines have five triple points and one double point, and the remaining three lines have four triple points and three double points. Taking the ideal of the triple points of these configurations we discover that, quite surprisingly, for one of the configurations the containment I(3)⊂I2 holds, while for the other it does not. Hence, for ideals of points defined by arrangements of lines, the (non)containment of a symbolic power in an ordinary power is not determined alone by arrangemental combinatorial features of the configuration. Moreover, for the configuration with the non-containment I(3)⊈I2, we examine its parameter space, which turns out to be a rational curve, and thus establish the existence of a rational non-containment configuration of points. Such rational examples are very rare

Geproci sets and the combinatorics of skew lines in P3\mathbb P^3

Geproci sets of points in $\mathbb P^3$ are sets whose general projections to $\mathbb P^2$ are complete intersections. The first nontrivial geproci sets came from representation theory, as projectivizations of the root systems $D_4$ and $F_4$. In most currently known cases geproci sets lie on very special unions of skew lines and are known as half grids. For this important class of geproci sets we establish fundamental connections with combinatorics, which we study using methods of algebraic geometry and commutative algebra. As a motivation for studying them, we first prove Theorem A: for a nondegenerate $(a,b)$-geproci set $Z$ with $d$ being the least degree of a space curve $C$ containing $Z$, that if $d\leq b$, then $C$ is a union of skew lines and $Z$ is either a grid or a half grid. We next formulate a combinatorial version of the geproci property for half grids and prove Theorem B: combinatorial half grids are geproci in the case of sets of $a$ points on each of $b$ skew lines when $a\geq b-1\geq 3$. We then introduce a notion of combinatorics for skew lines and apply it to the classification of single orbit combinatorial half grids of $m$ points on each of 4 lines. We apply these results to prove Theorem C, showing, when $n\gg m$, that half grids of $m$ points on $n$ lines with two transversals must be very special geometrically (if they even exist). Moreover, in the case of skew lines having two transversals, our results provide an algorithm for enumerating their projective equivalence classes. We conjecture there are $(m^2-1)/12$ equivalence classes of combinatorial $[m,4]$-half grids in the two transversal case when $m>2$ is prime.Comment: 36 page

Negative curves on special rational surfaces

We study negative curves on surfaces obtained by blowing up special configurations of points in P2. Our main results concern the following configurations: very general points on a cubic, 3–torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention

On the non-existence of orthogonal instanton bundles on P^{2n+1}

In this paper we prove that there do not exist orthogonal instanton bundles on P^{2n+1} . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle on P^{2n+1}