A counterexample to a conjecture on linear systems on .
A simplified proof of desingularization and applications.
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of desingularization of families of embedded schemes, and a formulation of desingularization which is stronger than Hironaka's). Our proof avoids the use of the Hilbert-Samuel function and Hironaka's notion of normal flatness: First we define a procedure for principalization of...
Calculation of Rozansky-Witten invariants on the Hilbert schemes of points on a K3 surface and the generalised kummer varieties.
Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic.
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.
Multidimensional term indexing for efficient processing of complex queries
The area of Information Retrieval deals with problems of storage and retrieval within a huge collection of text documents. In IR models, the semantics of a document is usually characterized using a set of terms. A common need to various IR models is an efficient term retrieval provided via a term index. Existing approaches of term indexing, e. g. the inverted list, support efficiently only simple queries asking for a term occurrence. In practice, we would like to exploit some more sophisticated...
Numerical evidence for a conjecture in real algebraic geometry.
Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro.
Subvarieties of the Hyperelliptic Moduli Determined by Group Actions
2000 Mathematics Subject Classification: 14Q05, 14Q15, 14R20, 14D22.Let Hg be the moduli space of genus g hyperelliptic curves. In this note, we study the locus Hg (G,σ) in Hg of curves admitting a G-action of given ramification type σ and inclusions between such loci. For each genus we determine the list of all possible groups, the inclusions among the loci, and the corresponding equations of the generic curve in Hg (G, σ). The proof of the results is based solely on representations of finite subgroups...