arXiv subjects
Publications and source records attributed to D. Arcara.
We prove that all monomials of $κ$-classes and $ψ$-classes are independent in $R^k(\ocM_{g,n})/R^k(\partial\ocM_{g,n})$ for all $k \leq [g/3]$. We also give a simple argument for $κ_l \neq 0$ in $R^l(\mathcal{M}_g)$ for $l \leq g-2$.
Mumford proved that psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g = 0 in the Chow ring of M_{g,1} [Mum83]. We find an explicit recursive formula for psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g in the tautological ring of \Mbar_{g,1} as a combination of classes supported on boundary strata.
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
A new tautological equation of $\Mbar_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.
We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use extensions of a line bundle L by O_C and the associated `forgetful' map to study a compactification of the moduli space of semi-stable vector bundles of rank 2 and determinant L on C.
We produce a lower bound for the dimension of the base locus of the generalized theta divisor on the moduli space SU_C(r) of semistable vector bundles of rank r and trivial determinant on a smooth curve C of genus g > 1.