On Certain Definite Integrals.
On certain Galois representations related to the modular curve
On Certain Numbers Associated to Isolated Critical Points.
On certain plane curves with many integral points.
On certain reduction problems concerning Abelian surfaces.
On Certain Representations of Semi-Simple Algebraic Groups and the Arithmetic of the Corresponding Invariants.
On certain rigid fibered Calabi-Yau threefolds.
On certain twisted families of elliptic curves of rank 8.
On Chebyshev polynomials and maximal curves
On chiral differential operators over homogeneous spaces.
On Chow rings of fine moduli spaces of modules.
On classical invariant theory and binary cubics
Let be a reductive complex algebraic group, and let denote the algebra of invariant polynomial functions on the direct sum of copies of the representations space of . There is a smallest integer such that generators and relations of can be obtained from those of by polarization and restitution for all . We bound and the degrees of generators and relations of , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
On classification of real singularities.
On classification of semigroup rings.
On Clifford's theorem for rank-3 bundles.
In this paper we obtain bounds on h0(E) where E is a semistable bundle of rank 3 over a smooth irreducible projective curve X of genus g ≥ 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s1(E), s2(E). We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.
On codimension-two subvarieties of hypersurfaces.
On Cohen-Macaulay modules over non-commutative surface singularities
We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.
On cohomological systems of Galois representations
The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead to interesting...
On commutativity and ovals for a pair of symmetries of a Riemann surface
We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry having g+1-q...
On commuting polynomial automorphisms of C2.
We charocterize the commuting polynomial automorphisms of C2, using their meromorphic extension to P2 and looking at their dynamics on the line at infinity.