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We extend the notion of basic classes (for the Donaldson invariants) to 4-manifolds with b+ > 1 which are (potentially) not of simple type or satisfy b1 > 0.We also give a structure theorem for the Donaldson invariants of 4-manifolds with b+ >[...]texto impreso
We introduce the different focal loci (focal points, planes and hyperplanes) of (n - 1)-dimensional families (congruences) of lines in P-n and study their invariants, geometry and the relation among them. We also study some particular congruence[...]texto impreso
Congruences of lines in P3, i.e. two-dimensional families of lines, and their focal surfaces, have been a popular object of study in classical algebraic geometry. They have been considered recently by several authors as Arrondo, Goldstein, Sols,[...]texto impreso
We determine the Fukaya-Floer (co)homology groups of the three-manifold y = S x S 1 , where S is a Riemann surface of genus g > 1. These are of two kinds. For the 1-cycle S1 C Y, we compute the Fukaya-Floer cohomology HFF*(Y, S1) and its ring s[...]texto impreso
Let ?:P?M be a principal G-bundle. Then one can consider the following diagram of fibre bundles: \CD J^{1}(P) @> \pi_{10}> > P\\ @VqVV @VV\pi V\\ C(P) @> p> > M\endCD where p is the bundle of connections of ?. As is well known, q is also a pri[...]texto impreso
We prove that the vanishing spheres of the Lefschetz pen- cils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplec- tomorphism group of the fiber. More precisely, a number of generaliz[...]texto impreso
Following our work in [18], we prove a gluing formula for the Donaldson nvariants of the connected sum of two four-manifolds along surfaces of the same genus g, self-intersection zero and representing odd homology classes,solving a conjecture of[...]texto impreso
Let C?M be the bundle of connections of a principal bundle on M . The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density ? on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle [...]texto impreso
Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifol[...]texto impreso
Let E be a holomorphic vector bundle over a compact connected Riemann surface X. The vector bundle E admits a holomorphic projective connection if and only if for every holomorphic direct summand F of E of positive rank, the equality degree(E)=r[...]texto impreso
Let C be a smooth projective curve of genus g > = 2 over C. Fix n > = 1, d is an element of Z. A pair (E, phi) over C consists of an algebraic vector bundle E of rank n and degree d over C and a section phi is an element of H-0(E). There is a co[...]texto impreso
Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | International Press | 2004Let R be either the Grothendieck semiring (semigroup with multiplication) of complex quasi-projective varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class \L of the complex affine line. We defin[...]texto impreso
Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María ; Scheiderer, Claus | International Press | 2006Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of th[...]texto impreso
Parameter invariance of the variational problem associated to the squared curvature Lagrangian, whose extremals are the elasticae, allows us to find an equivalent,nonparametric variational problem which is regular. Hamiltonian formalism is then [...]
