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2 votes
0 answers
174 views

Perverse sheaves and maximal genus Gopakumar-Vafa invariants

Let $f: X \to Y$ be a proper morphism between complex varieties (the varieties as well as the map may be non-smooth) and let $\phi \in \text{Perv}(X)$ be a perverse sheaf on $X$. Given this data, it ...
Benighted's user avatar
  • 1,701
8 votes
1 answer
665 views

References for quivers and derived categories of coherent sheaves for a string theory student

I'm a student mostly from physics knowledge hoping to learn about the math involved the string theory paper Topological Quiver Matrix Models and Quantum Foam. Context: The topological string theory ...
Ramiro Hum-Sah's user avatar
4 votes
0 answers
211 views

Bridgeland stability for restricted Kahler moduli?

Let $X$ be a simply-connected, smooth, projective Calabi-Yau threefold. To my understanding, Bridgeland introduced stability conditions on triangulated categories to give a proper mathematical ...
Benighted's user avatar
  • 1,701
6 votes
1 answer
967 views

Does there exists a Fukaya category with no objects

... and really without even the possibility of having objects, so it's not a matter of just finding the "correct" flavour of Fukaya category to use. Question: Does there exist interesting symplectic ...
Nati's user avatar
  • 1,981
7 votes
0 answers
299 views

Automorphism that the Fukaya category is "blind" to

Given a symplectic manifold $(M,\omega)$, there is a natural map $$ Symp(M,\omega) \to Auteq(D^\pi Fuk(M,\omega))$$ which sends a symplectic automorphism to the $A_\infty$-functor it induces on the ...
Nati's user avatar
  • 1,981
3 votes
2 answers
304 views

Examples of $1$-Calabi-Yau triangulated categories

Can you give me examples of $1$-Calabi-Yau triangulated categories $D$ different from the bounded derived category of coherent sheaves on an elliptic curve? I would like moreover the numerical ...
user97971's user avatar