Eine Bemerkung zur Existenz spezieller Divisoren auf glatten projektiven Kurven.
Elliptic curves on spinor varieties
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
Elliptic GW invariants of blowups along curves and surfaces.
Embedding-obstruction for products of non-singular, projective varieties.
Embeddings of general blowing-ups at points.
Enumeration of real conics and maximal configurations
We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in is maximal. That is, there exist generic configurations of real linear spaces such that all complex conics passing through these constraints are actually real.
Enumerative formulae for ruled cubic surfaces and rational quintic curves.
Enumerative geometry of degeneracy loci
Enumerative geometry of divisorial families of rational curves
We compute the number of irreducible rational curves of given degree with 1 tacnode in or 1 node in meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree passing through given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.
Enumerative geometry of singular plane curves.
Equivalence problem for minimal rational curves with isotrivial varieties of minimal rational tangents
We formulate the equivalence problem, in the sense of É. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form an isotrivial family. The main question in this case is for which projective variety , a family of minimal rational curves with -isotrivial varieties of minimal rational tangents...
Espaces projectifs anisotropes
Espaces projectifs anisotropes
Estimates of the number of rational mappings from a fixed variety to varieties of general type
First we find effective bounds for the number of dominant rational maps between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type , where , is the canonical bundle of and are some constants, depending only on .Then we show that for any variety there exist numbers and with the following properties:For any threefold of general type the number of dominant rational maps is bounded above by .The number of threefolds , modulo birational...
Even sets of nodes on sextic surfaces
We determine the possible even sets of nodes on sextic surfaces in , showing in particular that their cardinalities are exactly the numbers in the set . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification of existence...
Experimentation and conjectures in the real Schubert calculus for flag manifolds.
Factorization of point configurations, cyclic covers, and conformal blocks
We describe a relation between the invariants of ordered points in projective -space and of points contained in a union of two linear subspaces. This yields an attaching map for GIT quotients parameterizing point configurations in these spaces, and we show that it respects the Segre product of the natural GIT polarizations. Associated to a configuration supported on a rational normal curve is a cyclic cover, and we show that if the branch points are weighted by the GIT linearization and the rational...
Faisceaux triangulaires sur l'espace projectif
Families of algebraic curves with nodes
Familles maximales de systèmes de ponts surabondants dans P2.