269 research outputs found
Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane
A cubic surface in is known to contain 27 lines, out of which one can
form 36 Schlafli double - sixes i.e., collections of 12 lines such that each meets only and does
not meet . In 1881 F. Schur proved that any double - six gives
rise to a certain quadric , called Schur quadric which is characterized as
follows: for any the lines and are orthogonal with respect to
(the quadratic form defining) . The aim of the paper is to relate Schur's
construction to the theory of vector bundles on and to generalize this
construction along the lines of the said theory.Comment: 27 pages, plain TE
On the rationality of the moduli space of L\"uroth quartics
We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space
of quartics which can be circumscribed around a complete pentagon of lines
modulo the action of PGL_3(CC) is rational, as is the related moduli space of
Bateman seven-tuples of points in P^2.Comment: 7 page
Algebraic entropy and the space of initial values for discrete dynamical systems
A method to calculate the algebraic entropy of a mapping which can be lifted
to an isomorphism of a suitable rational surfaces (the space of initial values)
are presented. It is shown that the degree of the th iterate of such a
mapping is given by its action on the Picard group of the space of initial
values. It is also shown that the degree of the th iterate of every
Painlev\'e equation in sakai's list is at most and therefore its
algebraic entropy is zero.Comment: 10 pages, pLatex fil
Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg models
We prove that Hori--Vafa mirror models for smooth Fano complete intersections
in weighted projective spaces admit an interpretation as Laurent polynomials.Comment: 5 pages; several minor changes has been mad
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