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Existence of covers with fixed ramification in positive characteristic
Existence of covers fixed ramification positive characteristic Algebraic Geometry
2012/6/25
We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines br...
Existence of good moduli spaces for A_k-stable curves
Existence of good moduli spaces A_k-stable curves Algebraic Geometry
2012/6/25
We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a weak analog of the Keel-Mori theorem, which guarantees the existence of a coarse mo...
Existence des diviseurs dicritiques, d'apres S.S.Abhyankar
Existence des diviseurs dicritiques d'apres S.S.Abhyankar Algebraic Geometry
2012/4/18
In geometric terms, given a singular foliation of the plane, a dicritical divisor is (whenever it exists) an irreducible component of the exceptional divisor which is transverse to the foliation. Abhy...
On the existence of curves with $A_k$-singularities on $K3$-surfaces
versal deformations tacnodes Severi varieties K3 surfaces Ak-singularities
2011/9/19
Abstract: Let $(S,H)$ be a general primitively polarized $K3$ surface. We prove the existence of curves in $|\mathcal O_S(nH)|$ with $A_k$-singularities and corresponding to regular points of the equi...