p-adic zeros of polynomials.
Parabolic bundles, elliptic surfaces and SU (2)-representation spaces of genus zero Fuchsian groups.
Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants
The set of conjugacy classes appearing in a product of conjugacy classes in a compact, -connected Lie group can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety , where is the complexification of and is a maximal parabolic subgroup. This generalizes the results for of Agnihotri and the second author and Belkale on...
Parabolic sheaves on higher dimensional varieties.
Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator
Let be a family of rational polytopes parametrized by inequations. It is known that the volume of is a locally polynomial function of the parameters. Similarly, the number of integral points in is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it.
Parameter spaces for quadrics
The parameter spaces for quadrics are reviewed. In addition, an explicit formula for the number of quadrics tangent to given linear subspaces is presented.
Parameterizations of algebraic curves.
Parametrization of low-degree points on a Fermat curve
Parametrization of Möbius groups acting in a disk.
Parametrized solutions of Diophantine equations
Parity in Bloch’s conductor formula in even dimension
For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of -adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.
Parity sheaves, moment graphs and the -smooth locus of Schubert varieties
We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.
Partial flag varieties and preprojective algebras
Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .
Partial flags and parabolic group actions.
Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal form.
Partial intersections and graded Betti numbers.
Partial resolutions of quotient singularities.
Partialbruchzerlegung rationaler Functionen eines algebraischen Gebildes zweier Veränderlichen
Partielle Differentialgleichungen der hyperelliptischen Thetafunctionen und der Perioden derselben.
Parusinski's “Key Lemma” via algebraic geometry.