Abstract In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective
surfaces is lifted to oriented C^* C∗-equivariant cohomology theories. Here we study the K …

We compute tautological integrals over Quot schemes on curves and surfaces. After
obtaining several explicit formulas over Quot schemes of dimension-0 quotients on curves …

We study virtual invariants of Quot schemes parametrizing quotients of dimension at most 1
of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecture that the …

We conjecture a formula for the generating function of virtual χ _y χ y-genera of moduli
spaces of rank 2 sheaves on arbitrary surfaces with holomorphic 2-form. Specializing the …

An enumerative invariant theory in algebraic geometry, differential geometry, or
representation theory, is the study of invariants whichcount'$\tau $-(semi) stable objects $ E …

We initiate a systematic study on the cohomology rings of the moduli stack $\mathfrak {M} _
{d,\chi} $ of semistable one-dimensional sheaves on the projective plane. We introduce a set …

We study punctual quot-schemes of torsion-free sheaves $ E_Y $ on smooth projective
curves, surfaces and Calabi--Yau fourfolds via their virtual geometry. Our goal is to give a …

We compute the rational homology of the moduli stack $\mathcal {M} $ of objects in the
derived category of certain smooth complex projective varieties $ X $ including toric …

We survey here the construction and the basic properties of descendent invariants in the
theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the …

We conjecture a formula for the virtual elliptic genera of moduli spaces of rank 2 sheaves on
minimal surfaces $ S $ of general type. We express our conjecture in terms of the Igusa cusp …