Searcharxiv⌕ Search

arXiv subjects

Anca Mustata

Publications and source records attributed to Anca Mustata.

5 recordsLinked to original sources
arXiv2021

Singular plane sections and the conics in the Fermat quintic threefold

We present explicit equations for the space of conics in the Fermat quintic threefold $X$, working within the space of plane sections of $X$ with two singular marked points. This space of two-pointed singular plane sections has a birational morphism to the space of bitangent lines to the Fermat quintic threefold, which in its turn is birational to a 625-to-1 cover of $\PP^4.$ We illustrate the use of the resulting equations in identifying special cases of one-dimensional families of conics in $X.$

math.AG↗
arXiv2015

Gromov-Witten invariants for varieties with C* action

For any smooth projective variety with a C* action, we reduce the problem of computing its Gromov-Witten invariants to the similar problem for its fixed locus. Starting from the stacky version of variation of GIT for our variety, we construct the building blocks for the fixed loci of the moduli space of stable maps. We use this construction to compute their contribution to the virtual fundamental class.

math.AG↗
arXiv2010

A universal étale lift of a proper local embedding

To any finite local embedding of Deligne--Mumford stacks $g: Y\to X$ we associate an étale, universally closed morphism $F_{Y/X}\to X$ such that for the complement $Y^2_X$ of the image of the diagonal $Y \to Y\times_XY$, the stack $F_{Y^2_X/Y}$ admits a canonical closed embedding in $F_{Y/X}$, and $F_{Y/X}\times_XY$ is a disjoint union of copies of $F_{Y^2_X/Y}$. The stack $F_{Y/X}$ has a natural functorial presentation, and the morphism $F_{Y/X}\to X$ commutes with base-change. The image of $Y^2_X$ in $Y$ is the locus of points where the morphism $Y \to g(Y)$ is not smooth. Thus for many practical purposes, the morphism $g$ can be replaced in a canonical way by copies of the closed embedding $F_{Y^2_X/Y}\to F_{Y/X}$.

math.AG↗
arXiv2006

The Chow ring of Mbar_{0,m}(n, d)

We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points Mbar_{0,m}(n,d) as the subring of invariants of a ring B, relative to the action of the group of symmetries of d elements. B is computed by following a sequence of intermediate spaces for Mbar_{0,m}(n,d) and relating them to substrata of Mbar_{0,1}(n,d+m-1). An additive basis for the Chow ring is presented.

math.AG↗