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1 vote
0 answers
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Perfect complexes in a family

Consider a simple normal crossings variety $X=\bigcup_{i=1}^k X_i$ over $\mathbb{C}$ where $X_i$ are smooth projectiv and a flat family $\mathcal{X}\xrightarrow{\pi}\mathbb{A}^1_{\mathbb{C}}$ with $\...
TheWildCat's user avatar
2 votes
0 answers
336 views

Stability notion to smoothing varieties under a flat deformation with a smooth total space

Is there any stability notion that led to an algebraic variety be smoothable in general for Fano varieties or for Calabi-Yau varieties? Note that Friedman found a nesessary condition that $X$ to be ...
user avatar
10 votes
1 answer
534 views

Reference or explanation: Cup products, deformations of complex structure and Mirror Symmetry

In section 0.3. of their paper "Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields," Barannikov and Kontsevich discuss the fact that Kontsevich's formality morphism (from his paper ...
Johan Alm's user avatar
  • 141
8 votes
1 answer
469 views

Looking for a particular family of C.Y quintics

It is possible to construct (in many ways) a family of Calabi-Yau quintics $\mathcal{X}\rightarrow \Delta$, over disk, such that the fiber over $0$ has a singularities locally given by the equation $...
Mohammad Farajzadeh-Tehrani's user avatar