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DTSTART;TZID=America/New_York:20211012T130000
DTEND;TZID=America/New_York:20211012T140000
DTSTAMP:20260621T052358
CREATED:20240214T053342Z
LAST-MODIFIED:20240304T063443Z
UID:10002540-1634043600-1634047200@cmsa.fas.harvard.edu
SUMMARY:Derived projectivizations of two-term complexes
DESCRIPTION:Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack)\, there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk\, we first show that these three definitions are equivalent. Second\, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third\, we apply these results to various moduli situations\, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed\, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.
URL:https://cmsa.fas.harvard.edu/event/derived-projectivizations-of-two-term-complexes/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
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DTSTART;TZID=America/New_York:20211019T130000
DTEND;TZID=America/New_York:20211019T140000
DTSTAMP:20260621T052358
CREATED:20240214T053044Z
LAST-MODIFIED:20240304T063307Z
UID:10002539-1634648400-1634652000@cmsa.fas.harvard.edu
SUMMARY:D-critical structure(s) on Quot schemes of points of Calabi-Yau 3-folds
DESCRIPTION:Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015\, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes\, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem\, and new results in this direction\, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.
URL:https://cmsa.fas.harvard.edu/event/d-critical-structures-on-quot-schemes-of-points-of-calabi-yau-3-folds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T130000
DTEND;TZID=America/New_York:20211026T140000
DTSTAMP:20260621T052358
CREATED:20240214T062643Z
LAST-MODIFIED:20240304T063155Z
UID:10002549-1635253200-1635256800@cmsa.fas.harvard.edu
SUMMARY:On singular Hilbert schemes of points
DESCRIPTION:Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.
URL:https://cmsa.fas.harvard.edu/event/on-singular-hilbert-schemes-of-points/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
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