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Let F be the complete °ag variety over SpecZ with the tautological
ˉltration 0 ½ E1 ½ E2 ½ ￠ ￠ ￠ ½ En = E of the trivial bundle E of rank
n over F. The trivial hermitian metric o...
HEIGHT FORMULAS FOR HOMOGENEOUS VARIETIES
HOMOGENEOUS VARIETIES Differential and integral calculus
2015/12/17
We use classicalSchubert calculus to evaluate the integral formula
of Kaiser and Kohler [KK] for the Faltings height of certain homogeneous
varieties in terms of combinatorial data, and verify thei...
Let G be a semisimple complex algebraic group and P a parabolic subgroup of G.
The homogeneous space X = G=P is a projective complex manifold. My aim in
this lecture is to survey what is known about...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF SYMPLECTIC FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
2015/12/17
Let X = Sp2n/B the flag variety of the symplectic group. We
propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of t...
AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
2015/9/29
A natural family of affine cubic surfaces arises from
SL(2)-characters of the 4-holed sphere and the 1-holed torus. The
ideal locus is a tritangent plane which is generic in the sense that
the...
ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES
JOHNSON-TORELLI mapping class group
2015/9/29
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the
mapping class group MCG of Σ acts on the relative SU(2)-cha...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
2015/9/29
When G is a connected compact Lie group, and π
is a closed surface group, then Hom(π, G)/G contains an open
dense Out(π)-invariant subset which is a smooth symplectic manifold.
Unification and projectivity in Fregean varieties
unification projectivity Fregean varieties
2011/1/18
In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity....
The varieties of tangent lines to hypersurfaces in projective spaces
varieties of tangent lines hypersurfaces projective spaces
2011/1/20
or a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicit...
Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
hyperplane arrangement Milnor fiber monodromy polynomial-count
2011/1/19
A necessary and sufficient condition for the triviality of the Milnor monodromy of a central hyperplane arrangement is given. This is a consequence of a Thom-Sebastiani type result, where the sum of h...
Projective completions of affine varieties via degree-like functions
Projective completions of affine varieties degree-like functions
2011/1/18
We introduce and study a class of projective completions of ane algebraic varieties which generalize the construction of toric varieties from convex rational polytopes.
Vector Bundles over Normal Varieties Trivialized by Finite Morphisms
Essentially finite vector bundles finite mor-phisms principal bundles
2010/12/13
Let Y be a normal and projective variety over an algebraically closed field k and V a vector bundle over Y . We prove that if there exist a k-scheme X and a finite surjective morphism g : X → Y that t...
Lifting, restricting and sifting integral points on affine homogeneous varieties
integral points affine homogeneous varieties
2010/12/13
In [GN2] an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean e...
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a de...
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
Cohomology Toric Varieties Local Monomial Supports
2010/11/1
We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each com...