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Embedded $\mathbf{Q}$-Resolutions for Yomdin-Lê Surface Singularities
Quotient singularity weighted blow-up embedded Q-reso-lution Yomdin-Le singularity characteristic polynomial monodromy
2012/6/19
In a previous work we have introduced and studied the notion of embedded $\mathbf{Q}$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singulariti...
On a Newton filtration for functions on a curve singularity
Newton filtration functions curve singularity Algebraic Geometry
2012/6/9
In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the di...
For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent s...
Window shifts, flop equivalences and Grassmannian twists
Window shifts flop equivalences Grassmannian twists Algebraic Geometry
2012/6/14
We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seid...
We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether al...
On the operad structure of admissible G-covers
Algebraic Geometry structure of admissible G-covers
2012/5/25
We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible $G$-cover. To do this we are forced to introduce the notion of an operad colored not ...
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...
Singularities of the moduli space of level curves
Singularities moduli space of level curves Algebraic Geometry
2012/5/9
For a fixed integer l>1, we describe the singular locus of the compactification of the moduli space R_{g,l} of curves of genus g paired with an l-torsion point in their Jacobian. Generalizing previous...
Explicit presentations of nonspecial line bundles and secant spaces
algebraic curve nonspecial line bundle nonspecial divisor minimal presentation q-very ample order of very ampleness
2012/5/9
A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, ...
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...
This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and...
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
Lagrangian fibrations blowups of toric varieties mirror symmetry hypersurfaces Algebraic Geometry
2012/5/9
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
2012/5/9
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the...
Configuration types and cubic surfaces
Fat points free resolution cubic surface matroid Hilbert function
2012/4/16
This paper is a sequel to the paper \cite{refGH}. We relate the matroid notion of a combinatorial geometry to a generalization which we call a configuration type. Configuration types arise when one cl...
Let K denote an algebraically closed field. We study the relation between an ideal I in K[x1,...,xn] and its cross sections I_a=I+. In particular, we study under what conditions I can be recover...