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Local invariants on quotient singularities and a genus formula for weighted plane curves
Local invariants quotient singularities genus formula weighted plane curves Algebraic Geometry
2012/6/30
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
Rational cubic fourfolds containing a plane with nontrivial Clifford invariant
Rational cubic fourfolds nontrivial Clifford invariant Algebraic Geometry
2012/5/9
We isolate a general class of smooth rational cubic fourfolds containing a plane whose associated quadric surface bundle does not have a rational section. Equivalently, the Brauer class of the even Cl...
The classification of semi-stable plane sheaves supported on sextic curves
semi-stable sheaves moduli space sheaves supported on plane curves
2012/5/24
We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients m...
A remark on Waring decompositions of some special plane quartics
remark Waring decompositions special plane quartics Algebraic Geometry
2012/4/16
This paper concerns Waring decompositions of a certain kind of plane quartics of high rank. The main result is the following. Let x, l_1, ...., l_7 be linear forms and q a quadratic form on a K-vector...
Linear systems associated to unicuspidal rational plane curves
Linear systems associated unicuspidal rational plane curves
2012/2/29
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane cur...
Cuspidal plane cuves, syzygies and a bound on the MW-rank
Elliptic threefolds Mordell-Weil rank Alexander polynomials of plane curves
2011/9/1
Abstract: Let $C=Z(f)$ be a reduced plane curve of degree $6k$, with only nodes and ordinary cusps as singularities. Let $I$ be the ideal of the points where $C$ has a cusp. Let $\oplus S(-b_i)\to \op...
Poincare series for plane curve singularities and their behaviour under projections
Curve singularity Alexander polynomial Poincare series value semigroup Grothendieck ring of varieties
2011/8/26
Abstract: Our purpose is to investigate all defined Poincar\'e series associated with multi-index filtrations and value semigroups of curve singularities---not necessarily complex---with regard to the...