IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Tue, 20 Apr 2021 00:56:38 GMT2021-04-20T00:56:38Z10191Computing the number of apparent double points of a surfacehttp://hdl.handle.net/11585/213638Titolo: Computing the number of apparent double points of a surface
Abstract: For a smooth surface S ⊂ P^5 there are well known classical formulas giving the number ρ(S) of secants of S passing through a generic point of P^5. In this paper, for possibly singular surfaces T, a computer assisted computation of ρ(T) from the defining ideal I(T) ⊂ K[x_0,...,x_5] is proposed. It is based on the Stückrad-Vogel self-intersection cycle of T and requires the computation of the normal cone of the ruled join J(T, T) along the diagonal. It is shown that in the case when T ⊂ P^5 arises as the linear projection with center L of a surface S ⊂ P^N (N > 5) (which satisfies some mild assumptions), the computational complexity can be reduced considerably by using the normal cone of Sec S along
L ∩ Sec S instead of the former normal cone. Many examples and the relative code for the computer algebra systems REDUCE, CoCoA, Macaulay2 and Singular are given.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/2136382013-01-01T00:00:00ZA degree formula for secant varieties of curveshttp://hdl.handle.net/11585/339920Titolo: A degree formula for secant varieties of curves
Abstract: Using the Stückrad-Vogel self-intersection cycle of an irreducible and reduced curve in projective space, we obtain a formula that relates the degree of the secant variety, the degree and the genus of the curve and the self-intersection numbers, the multiplicities and the number of branches of the curve at its singular points. From this formula we deduce an expression for the difference between the genera of the curve. This result shows that the self-intersection multiplicity of a curve in projective N-space at a singular point is a natural generalization of the intersection multiplicity of a plane curve with its generic polar curve. In this approach, the degree of the variety (up to a factor 2), the self-intersection numbers and the multiplicities of the singular points are leading coefficients of a bivariate Hilbert polynomial, which can be computed by computer algebra systems.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3399202014-01-01T00:00:00ZEnigmahttp://hdl.handle.net/11585/42592Titolo: Enigma
Abstract: Scheda di presentazione del film "Enigma" e degli argomenti matematici collegati (la macchina Enigma, i matematici e Enigma, Alan Turing, ecc), bibliografia per approfondimenti
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/425922005-01-01T00:00:00ZNumeri primi e crittografiahttp://hdl.handle.net/11585/809510.7Titolo: Numeri primi e crittografia
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/809510.72020-01-01T00:00:00ZOn the self-intersection cycle of surfaces and some classical
formulas for their secant varietieshttp://hdl.handle.net/11585/80758Titolo: On the self-intersection cycle of surfaces and some classical
formulas for their secant varieties
Abstract: We study the relation between certain local and global numerical invariants of a projective surface given by the Stückrad-Vogel self-intersection cycle. In the smooth case we find a relation between the degrees of the tangent, the secant and the first polar variety which generalizes classical relations between the so called elementary invariants of surfaces. For singular surfaces this relation involves also the contributions of singularities to the self-intersection cycle. In order to make the formula really effective for singular surfaces, we need to describe the movable part of the self-intersection cycle on the singular locus. This is done explicitly for a particular class of non normal del Pezzo surfaces.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11585/807582011-01-01T00:00:00ZIntersection numbers and characters of algebraic curves and surfaces: theory and computationhttp://hdl.handle.net/11585/151855Titolo: Intersection numbers and characters of algebraic curves and surfaces: theory and computation
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/1518552013-01-01T00:00:00ZGeneralized Samuel Multiplicities and Applicationshttp://hdl.handle.net/11585/30574Titolo: Generalized Samuel Multiplicities and Applications
Abstract: In this note we survey and discuss the main results on the multiplicity sequence we introduced in former papers as a generalization of Samuel's multiplicity. We relate this new multiplicity to other numbers introduced in different contests, for example the Segre numbers of Gaffney and Gassler and the Hilbert coefficients defined by Ciupercă. Discussing some examples we underline the usefulness of the multiplicity sequence for concrete calculations in algebraic geometry using computer algebra systems.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11585/305742006-01-01T00:00:00ZAlcune riflessioni su Fermat's Last Theoremhttp://hdl.handle.net/11585/13369Titolo: Alcune riflessioni su Fermat's Last Theorem
Abstract: Si trattta di un breve articolo espositivo sul film di S.Singh e J.Lynch "Fermat's Last Theorem", che narra la lunga storia del celebre teorema e della dimostrazione di A.Wiles.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/133692005-01-01T00:00:00ZMatematica e Cinema IIhttp://hdl.handle.net/11585/13374Titolo: Matematica e Cinema II
Abstract: Rassegna cinematografica dedicata alla matematica, in cui ogni proiezione era accompagnata da una conferenza/dibattito sui contenuti matematici del film.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11585/133742004-01-01T00:00:00ZMatematica e Teatrohttp://hdl.handle.net/11585/13378Titolo: Matematica e Teatro
Abstract: Rassegna di rappresentazioni teatrali dedicate alla matematica, in cui ogni spettacolo era seguito da una conferenza/dibattito sul testo rapppresentato e sui suoi contenuti matematici.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11585/133782004-01-01T00:00:00Z