Algorithmische P-Zerlegungen und Anwendungen
An Algorithm for Lifting Points in a Tropical Variety
Decomposable ternary cubics.
Maps of toric varieties in Cox coordinates
The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.
Note on the Solution of the Quartic Equation ..........
Rational intersection cohomology of projective toric varieties.
Sagbi bases of Cox–Nagata rings
We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective -space at points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D’Cruz–Iarrobino and Buczyńska–Wiśniewski....
The Hasse zeta function of a K3 surface related to the number of words of weight 5 in the Melas codes.
Welschinger invariants of small non-toric Del Pezzo surfaces
We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at real and pairs of conjugate imaginary points, where , and the real quadric blown up at pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants of real toric...
Zum Grad von Basis-Eliminationspolynomen und Resultanten