The connection between a conjecture of Carlisle and Kropholler, now a theorem of Benson and Crowley-Boevey, and Grothendieck's Riemannian-Roch and duality theorems.
The connection between the -theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
The ?-constant stratum is not smooth.
The construction of weight-two arithmetic cohomology.
The correspondence between Barsotti-Tate groups and Kisin modules when
Let be a finite extension over and the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over .
The covariant systems of Todd and Segre
The covering semigroup of invariant control systems on Lie groups
It is well known that the class of invariant control systems is really relevant both from theoretical and practical point of view. This work was an attempt to connect an invariant systems on a Lie group with its covering space. Furthermore, to obtain algebraic properties of this set. Let be a Lie group with identity and a cone in the Lie algebra of that satisfies the Lie algebra rank condition. We use a formalism developed by Sussmann, to obtain an algebraic structure on the covering...
The Cubo-Cubic Transformation of IP3 is Very Special.
The curve , is not set-theoretic complete intersection of two quartic surfaces
The cuspidal torsion packet on hyperelliptic Fermat quotients
Let be a prime, be the non-singular projective curve defined over by the affine model , the point of at infinity on this model, the Jacobian of , and the albanese embedding with as base point. Let be an algebraic closure of . Taking care of a case not covered in [12], we show that consists only of the image under of the Weierstrass points of and the points and , where denotes the torsion points of .
The cyclic homology and K-theory of curves.
The cylinder homomorphism associated to quintic fourfolds
The decomposition and specialization of algebraic families of vector bundles
The defect of weak approximation for homogeneous spaces
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The deformation theory of representations of fundamental groups of compact Kähler manifolds
The degree at infinity of the gradient of a polynomial in two real variables
Let f:ℝ² → ℝ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient ∇f in terms of the real branches at infinity of the level curves {f(x,y) = λ} for some λ ∈ ℝ. The formula obtained is a counterpart at infinity of the local formula due to Arnold.
The degree of rational cuspidal curves.
The degree of the inverse of a polynomial automorphism.
The degree of the secant variety and the join of monomial curves.
A monomial curve is a curve parametrized by monomials. The degree of the secant variety of a monomial curve is given in terms of the sequence of exponents of the monomials defining the curve. Likewise, the degree of the join of two monomial curves is given in terms of the two sequences of exponents.