Some remarks on morphisms between Fano threefolds.
Some remarks on Set-theoretic Intersection Curves in
Motivated by the notion of Seshadri-ampleness introduced in [11], we conjecture that the genus and the degree of a smooth set-theoretic intersection should satisfy a certain inequality. The conjecture is verified for various classes of set-theoretic complete intersections.
Some results on the geometry of full flag manifolds and harmonic maps.
Some results on the syzygies of finite sets and algebraic curves
Some results on the topology of varieties dominated by Cn.
Some Results on Unirationality of Algebraic Surfaces.
Some theorems on generation of ideals in affine algebras.
Some zero-dimensional generic singularities ; finite algebras having small tangent space
Special line bundles on curves with involution.
Special linear systems and syzygies
Specialization of Segre classes of singular algebraic varieties.
Spherical Complexes and Nonprojective Tone Varieties.
Spherical conjugacy classes and the Bruhat decomposition
Let be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in as those intersecting only Bruhat cells in corresponding to involutions in the Weyl group of .
Spherical roots of spherical varieties
Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.
Spherical spaces for which the Hasse principle and weak approximation fail.
We construct spherical homogeneous spaces X of semisimple simply connected groups with connected stabilizers such that the Hasse principle or weak approximation fail for X.
Spherical varieties and Wahl’s conjecture
Using the theory of spherical varieties, we give a type independent very short proof of Wahl’s conjecture for cominuscule homogeneous varieties for all primes different from 2.
Springer's Weyl Group Representations Through Characteristc Classes of Cone Bundles.
Stabilization of monomial maps in higher codimension
A monomial self-map on a complex toric variety is said to be -stable if the action induced on the -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of , we can find a toric model with at worst quotient singularities where is -stable. If is replaced by an iterate one can find a -stable model as soon as the dynamical degrees of satisfy . On the other hand, we give examples of monomial maps , where this condition...
Stable rationality of certain PGLn-quotients.
Stably rational algebraic tori
The rationality of a stably rational torus with a cyclic splitting field is proved.