Good degeneration of Quot-schemes and coherent systems

By Jun Yu Li, Baosen Wu. 2011

85 citations recorded by the source corpus.

We construct good degenerations of Quot-schemes and coherent systems using the stack of expanded degenerations. We show that these good degenerations are separated and proper DM stacks of finite type. Applying to the projective threefolds, we derive degeneration formulas for DT-invariants of ideal sheaves and PT stable pair invariants.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/554a0a454101350b22825dac21cd7cc8a4b6e65a

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In Geometry and Topology

1. R. Pandharipande
2. A. Okounkov
3. Aaron Pixton
4. Davesh Maulik
5. D. Gaitsgory
6. Yukinobu Toda
7. Richard P. Thomas
8. Marcos Mariño

In Mathematical Physics

1. R. Pandharipande
2. A. Okounkov
3. Aaron Pixton
4. D. Gaitsgory
5. Davesh Maulik
6. Richard P. Thomas
7. C. Vafa
8. Yukinobu Toda

In Statistical and Nonlinear Physics

1. R. Pandharipande
2. A. Okounkov
3. D. Gaitsgory
4. Paul D. Johnson
5. J. Francis
6. Marcos Mariño
7. V. Bouchard

Citations in the corpus

• Gromov-Witten/pairs correspondence for the quintic 3-fold (2012, background): “See [13, 15, 18, 30] for a technical discussion of relative theories.”
• Sheaves of categories and the notion of 1-affineness (2013, background): “sheaves on the singular (special) fiber. One would like to relate these invariants to the so-called relative invariants of the Fano 3-folds relative to the K3 surface. For more details see the article [14] by J. Li and B. Wu and the references therein. The key feature of this example (discussed in [2”
• Lectures on K-theoretic computations in enumerative geometry (2015, methodology): “Their construction follows an established path in Gromov-Witten theory [51, 52] and, later, DT theory [53].”