# The DT/PT correspondence for smooth curves

@article{Ricolfi2018TheDC, title={The DT/PT correspondence for smooth curves}, author={Andrea T. Ricolfi}, journal={Mathematische Zeitschrift}, year={2018}, volume={290}, pages={699-710} }

We show a version of the DT/PT correspondence relating local curve counting invariants, encoding the contribution of a fixed smooth curve in a Calabi–Yau threefold. We exploit a local study of the Hilbert–Chow morphism about the cycle of a smooth curve. We compute, via Quot schemes, the global Donaldson–Thomas theory of a general Abel–Jacobi curve of genus 3.

#### 11 Citations

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Let $C$ be a hyperelliptic curve embedded in its Jacobian $J$ via an Abel-Jacobi map. We compute the scheme structure of the Hilbert scheme component of $\textrm{Hilb}_J$ containing the Abel-Jacobi… Expand

Higher rank motivic Donaldson-Thomas invariants of $\mathbb{A}^3$ via wall-crossing, and asymptotics

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On the motive of the Quot scheme of finite quotients of a locally free sheaf

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- 2019

Let $X$ be a smooth variety, $E$ a locally free sheaf on $X$. We express the generating function of the motives $[\textrm{Quot}_X(E,n)]$ in terms of the power structure on the Grothendieck ring of… Expand

Unweighted Donaldson-Thomas theory of the banana 3-fold with section classes.

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We further the study of the Donaldson-Thomas theory of the banana threefolds which were recently discovered and studied in [Bryan'19]. These are smooth proper Calabi-Yau threefolds which are fibred… Expand

The Donaldson-Thomas Theory of the Banana Threefold with Section Classes

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- 2020

We further the study of the Donaldson-Thomas theory of the banana threefolds which were recently discovered and studied in [Bryan'19]. These are smooth proper Calabi-Yau threefolds which are fibred… Expand

Virtual classes and virtual motives of Quot schemes on threefolds

- Mathematics
- 2019

For a simple, rigid vector bundle $F$ on a Calabi-Yau $3$-fold $Y$, we construct a symmetric obstruction theory on the Quot scheme $\textrm{Quot}_Y(F,n)$, and we solve the associated enumerative… Expand

Higher rank K-theoretic Donaldson-Thomas Theory of points

- Mathematics, Physics
- Forum of Mathematics, Sigma
- 2021

Abstract We exploit the critical structure on the Quot scheme $\text {Quot}_{{{\mathbb {A}}}^3}({\mathscr {O}}^{\oplus r}\!,n)$, in particular the associated symmetric obstruction theory, in order to… Expand

Framed motivic Donaldson-Thomas invariants of small crepant resolutions

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For an arbitrary integer $r\geq 1$, we compute $r$-framed motivic PT and DT invariants of small crepant resolutions of toric Calabi-Yau $3$-folds, establishing a "higher rank" version of the motivic… Expand

Framed sheaves on projective space and Quot schemes

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We prove that, given integers $m\geq 3$, $r\geq 1$ and $n\geq 0$, the moduli space of torsion free sheaves on $\mathbb P^m$ with Chern character $(r,0,\ldots,0,-n)$ that are trivial along a… Expand

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