arXiv subjects

Nicolò Sibilla

Publications and source records attributed to Nicolò Sibilla.

23 records · Page 2Linked to original sources

arXiv2015

Derived loop stacks and categorification of orbifold products

The existence of interesting multiplicative cohomology theories for orbifolds was first suggested by string theorists. Orbifold products have been intensely studied by mathematicians for the last fifteen years. In this paper we focus on the virtual orbifold product that was first introduced in Lupercio et al. (2007). We construct a categorification of the virtual orbifold product that leverages the geometry of derived loop stacks. By work of Ben-Zvi, Francis and Nadler, this reveals connections between virtual orbifold products and Drinfeld centers of monoidal categories, thus answering a question of Hinich.

math.AG↗

arXiv2014

The nonequivariant coherent-constructible correspondence and tilting

The coherent-constructible correspondence is a relationship between coherent sheaves on a toric variety X, and constructible sheaves on a real torus T. This was discovered by Bondal, and explored in the equivariant setting by Fang, Liu, Treumann and Zaslow. In this paper we collect partial results towards a proof of the non equivariant coherent-constructible correspondence. Also, we give applications to the construction of tilting complexes in the derived category of toric DM stacks.

math.AG↗

arXiv2013

Skeleta of Affine Hypersurfaces

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

math.AG↗

arXiv2012

A note on mapping class group actions on derived categories

Let $X_n$ be a cycle of $n$ projective lines, and $\bT_n$ a symplectic torus with $n$ punctures. Using the theory of spherical twists introduced by Seidel and Thomas (2001), I will define an action of the pure mapping class group of $\bT_n$ on $D^b(Coh(X_n))$. The motivation comes from homological mirror symmetry for degenerate elliptic curves, which was studied by the author with Treumann and Zaslow in arXiv:1103.2462 .

math.AG↗

arXiv2012

Mirror Symmetry in dimension one and Fourier-Mukai equivalences

In this paper we will describe an approach to mirror symmetry for appropriate 1-dimensional DM stacks of arithmetic genus $g \leq 1$, called tcnc curves, which was developed by the author with Treumann and Zaslow in arXiv:1103.2462 . This involves introducing a conjectural sheaf-theoretic model for the Fukaya category of punctured Riemann surfaces. As an application, we will investigate derived equivalences of tcnc curves, and generalize classic results of Mukai on dual abelian varieties (Mukai 1981).

math.AG↗